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  • Satellite Simulation
Cislunar Glossary
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Forum
Home
Gitee
GitHub
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  • Cislunar glossary (terms & definitions)

    • /en/glossary/
    • Fundamentals

      • Abnormal Extremal
      • Automatic Differentiation
      • Adaptive Grid Subdivision
      • Amplitude Parameter
      • An analytical approximation method for periodic orbits near libration points, developed by Richardson in 1980. It expands the equations of motion to third order about the libration point and uses the Lindstedt-Poincaré perturbation method to eliminate secular terms, yielding third-order analytical solutions for Halo orbits in both in-plane and out-of-plane components. This provides initial guesses for subsequent numerical differential correction and is the standard first step in Halo orbit computation.
      • Analytical Ephemeris
      • Augmented Earth-Moon Model
      • Augmented State Vector
      • Bang-off-Bang Thrust Profile
      • Barycentric Synodic Frame
      • Birkhoff Normal Form
      • Canonical Transformation
      • Center-of-Mass Rotating Frame
      • Chebyshev Polynomial
      • Coast Arc
      • Collinear Lagrange Point
      • Combined Chemical-Electric Propulsion Transfer
      • Conjugate point condition
      • Conjugate Point
      • Continuous Low Thrust
      • Control Regularization
      • Costate Equations
      • Costate
      • Cowell's Perturbation Method
      • Differential-Algebraic Equations
      • Declination Deviation
      • Delta-V Budget
      • Delta-v (Δv)
      • Differential Correction Algorithm
      • Differential Correction Method
      • Differential Correction
      • Dimensionality Reduction
      • Direct Method
      • CRTBP Nondimensional Units
      • Dynamic Reference Catalog
      • Earth-Fixed Coordinate System
      • Earth Gravity Field Model
      • Earth Oblateness
      • Eccentricity Sensitivity Analysis
      • Effective Potential
      • Effective Pseudo-Potential
      • EGM2008 Earth Gravity Model
      • Eigenvalue
      • Eigenvector
      • EME2000 Reference Frame
      • Energy Minimization
      • Engine Throttle Parameter
      • Entrywise Leading Order Interpolation
      • Equation of Motion
      • Electric Propulsion
      • Equilibrium Region
      • Euler-Hill Coordinate Frame
      • Exponential Instability
      • Fuel Exhaust Velocity
      • Full-Ephemeris Model
      • Global Analysis of Invariant Objects
      • Post-Newtonian Parameter, gamma
      • Gauss-Legendre Collocation Method
      • Geocentric Rotating Frame
      • Geocentric Rotating Polar Coordinate System
      • Geometric Optimal Control
      • GGM05C Earth Gravity Field Model
      • GL0660B Lunar Gravity Field Model
      • Global Search
      • Gauss Pseudospectral Method, GPM
      • Gravitational Asymmetry at Libration Points
      • Gravitational Light Deflection
      • Gravitational Potential
      • Gravity Field Model
      • Gravity gradient matrix
      • GRGM660PRIM Lunar Gravity Field Model
      • Grid Search Method
      • Grid Search
      • Hamiltonian Integrable Approximation
      • Hamiltonian
      • Heterogeneous Constellation
      • Hidden-Genes Genetic Algorithm
      • High-Fidelity Simulation
      • Hill Frame
      • Hill Region Configuration
      • Hill Region
      • Homotopy Iteration Method
      • Homotopy Method / Homotopic Approach
      • Homotopy Method
      • Hyperbolic Manifold
      • Ill-Conditioned State Transition Matrix
      • Improved Bi-Circular Model
      • Impulse Direction Angle
      • In-Plane Amplitude
      • Indirect Method
      • Indirect Optimal Control
      • Invariant Torus
      • Intermediate thrust arc
      • Jacobi Field
      • Jacobian Matrix
      • Kolmogorov-Arnold-Moser Tori, KAM Tori
      • L2-L1 Homotopy
      • L3 Point
      • L4 Point
      • L5 Point
      • Lagrange Multiplier
      • Lagrange Point
      • Lambert Flight Time Theorem
      • Lambert's Algorithm
      • Lambert's Problem
      • Libration Point
      • Lindstedt-Poincaré Method
      • Lindstedt-Poincaré Series Expansion
      • Line of Nodes of the Lunar Orbit
      • Linearization
      • LME2000 Reference Frame
      • Local Truncation Error
      • Logarithmic Barrier Homotopy
      • Lorentz Contraction
      • Low-Thrust Control
      • Low-Thrust Propulsion
      • LP100K Model
      • LP150Q Lunar Gravity Model
      • Linear Time-Periodic System
      • Lunar Body-Fixed Frame
      • Lunar Equatorial Plane
      • Lunar Gravitational Potential
      • Lunar Gravity Field Irregularity
      • Lunar Gravity Field Model
      • Lunar Gravity Field
      • Lunar Orbit Eccentricity
      • Lunar Orbital Plane
      • Lunar Sub-Satellite Track
      • Lunar Synodic Period
      • Mapped Adjoint Control Transformation, MACT
      • Moon-Centered Inertial Frame
      • Method of Variation of Constants
      • Minimum Time of Flight, Min TOF
      • Modified Delaunay Variables
      • Moon-Centered Inertial Frame (MCI)
      • Maximum-thrust arc
      • Multi-Body Dynamical Environment
      • Multi-Conic Method
      • Multiple Shooting Method
      • Natural Continuation
      • Non-Spherical Gravitational Potential
      • Nondimensionalization
      • Normal Extremal
      • Normalized Parameter
      • Normalized Units
      • Non-Dominated Sorting Genetic Algorithm II
      • Null-thrust arc
      • Numerical Continuation
      • Numerical Ephemeris
      • Optimal Relative Motion Control
      • Orbital Axis Slewing
      • Orbital Coordinate System
      • Orthogonal coordinate system
      • Osculating Orbital Elements
      • Out-of-Plane Difference
      • Planar Circular Restricted Three-Body Problem
      • PDF Transformation Rule
      • Phase Parameter
      • Piecewise Polynomial Control
      • Pontryagin Minimum Principle
      • Pontryagin Optimality Conditions
      • Position Angle
      • Precession-Nutation Matrix
      • Precomputed Variational Data
      • Primer vector equation
      • Primer vector
      • Principal Axes Coordinate Frame
      • Pseudo-Potential Function
      • Pseudo-Potential
      • Pseudopotential
      • Quasi-Circular Transfer
      • Reconstructed Harmonic Balance Method
      • Richardson Third-Order Analytical Approximation
      • Richardson Third-Order Analytical Solution
      • Richardson Third-Order Expansion
      • Right Ascension Deviation
      • Runge-Kutta Method
      • Earth-Moon Barycentric Rotating Frame
      • Rotating Frame
      • Selenocentric Frame
      • Selenocentric Inertial Coordinate System
      • Selenocentric Instantaneous Earth-Moon Plane Coordinate Frame
      • Solar Electric Propulsion, SEP
      • Shape Parameter
      • Shooting Method
      • Single Shooting Method
      • Slack Variable
      • Small Denominator
      • Smoothing Technique
      • Surface of Section, SOS
      • Spherical Harmonic Expansion
      • Staggered Optimization
      • State Equation
      • A 6x6 matrix describing how perturbations propagate from initial to terminal state in a dynamical system. Its four sub-blocks represent partial derivative mappings for position-to-position (A), velocity-to-position (B), position-to-velocity (C), and velocity-to-velocity (D). In differential correction, the B and D sub-blocks provide sensitivities of terminal position and velocity to initial velocity, serving as the core mathematical tool for correction computation. The STM also yields the monodromy matrix for invariant manifold computation.
      • Strong Legendre Condition
      • Sun-B1 Rotating Frame
      • Sun-Earth-Moon System
      • Switching Function
      • Symplectic Matrix
      • Synodic Coordinates
      • Synodic Frame
      • Synodic Period
      • Synodic Reference Frame
      • Synodic Rotating Frame
      • Synodical Reference System
      • Tisserand-Poincaré Graph
      • Tangential Thrust
      • Terminal Performance Index
      • Thrust Magnitude
      • Time-Varying System
      • Transfer Leg
      • Truncation Strategy
      • Unscented Kalman Filter, UKF
      • Uncertainty Propagation
      • Variable-Time Targeting
      • Variational Equation
      • Variable-specific-impulse engine
      • Zero-Velocity Curve
    • Dynamics & math

      • 1/1 Orbital Resonance
      • 1-1 Resonance
      • 3-1-3 Euler Angle Sequence
      • A modified invariant manifold formed by applying a small velocity increment adjustment to the natural invariant manifold. Since the natural manifold's perilune distance usually does not match the target lunar orbit radius, an impulse at the Halo orbit injection point reshapes the manifold to satisfy the selenocentric distance constraint. Perturbed manifolds extend the transfer phase range beyond the two fixed points of natural zero-cost trajectories.
      • Absolute Phase Bias
      • Adjoint Control Transformation, ACT
      • Action-Angle Variables
      • Adams-Cowell Integrator
      • Adjoint-Control Transformation
      • Adjoint Equations
      • Adjoint Method
      • Augmented Lagrangian Iterative LQR, AL-iLQR
      • Allowable Control Set
      • Allowed Region
      • Amplitude Condition
      • Amplitude Correction Maneuver
      • An iterative method that maps terminal constraint residuals back to initial velocity corrections via the state transfer matrix. In libration point Halo orbit transfer design, it uses perilune distance and flight path angle as constraints, computing velocity increment corrections through partial derivatives decomposed by the state transfer matrix. The algorithm converges quickly for strongly nonlinear problems but is sensitive to initial guesses, requiring invariant manifolds to provide starting values.
      • Angle-Distance Section Method
      • Annual Station-Keeping Cost
      • Anti-Tangential Thrust
      • Adaptive Polynomial Chaos Expansion
      • Apogee Poincaré Section
      • Apse Map
      • Apse Poincare Map
      • Apsidal Transfer
      • Arnold Diffusion
      • Arnold Tori
      • Arrival Deflection Angle
      • Artificial Libration Point
      • Asymmetry
      • Asymptotic Tracking
      • Adaptive Trajectory Design Catalog
      • Atmospheric Drag Perturbation
      • Atmospheric Drag
      • Atmospheric Perturbation
      • Attitude Control Thruster
      • Augmented Lagrangian Method
      • Averaging Method
      • Axis Ratio
      • B-Spline Control Parameterization
      • Backward Integration Method
      • Backward Lunar Gravity Assist
      • Ballistic Arc
      • Ballistic Capture
      • Ballistic Transfer
      • Bang-bang Control (Bang-bang Control)
      • Bang-bang Solution
      • Bang-Bang Thrust Profile
      • Bang-off-Bang Control
      • Bang-off-Bang Thrust Profile
      • Barycentric Coordinate System
      • Barycentric Rotating Coordinate System
      • Barycentric Synodic Coordinate System
      • Battin-Giorgi Method
      • Battin-Vaughn Algorithm
      • Ballistic Coefficient
      • Bicircular Problem
      • Bicircular Restricted Four-Body Problem, BCR4BP
      • Bicircular Restricted Four-Body Problem
      • beluga
      • Bicircular Four-Body Problem
      • Bicircular Model
      • Bilinear Tangent Law
      • Birkhoff Equations
      • Birkhoff-Gustavson Normal Form
      • Birkhoff Normal Form
      • Blended CR3BP
      • Box Covering
      • Conley-McGehee Tube, C-M Tube
      • Cannon Ball Model
      • Canonical Coordinates
      • Canonical Equations
      • Capture Trajectory Classification
      • Cauchy-Green Tensor Method
      • Cell Estimation Technique
      • Center Manifold
      • Center-Saddle
      • Center Subspace
      • Central Configuration
      • Central Floquet Mode
      • Central Manifold Action Variable
      • Central Manifold
      • Chaotic Sea
      • Characteristic Curve
      • Characteristic Multiplier
      • Characteristic Parameter
      • CLERM
      • Jacobi Constant
      • Classification of Cislunar Trajectories
      • Close Lunar Flyby Plane Change Transfer
      • Constrained Markov Decision Process
      • Circular Non-linear Equations of Relative Motion, CNERM
      • Co-state Variables
      • Co-state
      • Codimension-1 Manifold
      • Collinear Libration Point
      • Collinear Libration Points
      • Collinear Singularity
      • Collision Belt
      • Collision Curve
      • Collocation with Optimization for Low-Thrust
      • Complete Uncertain Lambert Solutions
      • Conic Approximation of Transfer Segment
      • Conjugate Momenta
      • Conjugate Point Mapping
      • Conjugate Variables
      • Conley-McGehee Tube
      • Connection Point
      • Connection
      • Conservative System
      • Constrained Functional
      • Constrained Nonlinear Optimization
      • Constrained X-Axis Crossing Velocity
      • Constraint Conditions
      • Constraint Relaxation
      • Continuation Method (Parameter Continuation)
      • Continuation Parameter
      • Continuation Procedure
      • Continuation
      • Continuous Homotopy
      • Continuous Thrust Model
      • Continuous-Thrust Station-Keeping
      • Continuous Thrust
      • Control Curve (U_i)
      • Control Parametrization
      • Controllability
      • Convex Cone
      • Copenhagen Problem
      • Coriolis Theorem
      • Costate-Control Transformation
      • Costate Normalization
      • Costate Variable
      • Coupled CR3BP
      • Coupled Three-Body Problem
      • Coupling Maneuver
      • Coupling of RTBPs
      • Calculus of Variations
      • Cowell's Perturbation Technique
      • Compound Particle Swarm Optimization
      • CR3BP Lambert Problem
      • Circular Restricted Three-Body Problem (CR3BP)
      • Earth-Moon Three-Body Problem with Solar Perturbation
      • Cross-product Control
      • Circular Restricted Three-Body Problem with Low-Thrust, CRTBP-LT
      • CRTBP Mass Parameter
      • Circular Restricted Three-Body Problem
      • Cylindrical Isomorphic Mapping
      • Damped Bisection Correction
      • Direct Collocation with Nonlinear Programming
      • Differential Evolution
      • Debris Cloud Evolution
      • Defect Constraint
      • Delaunay Elements
      • Delaunay Variables
      • Departure Velocity
      • Deviation
      • Drag-Free and Attitude Control, DFAC
      • Direct Fly-By Transfer, DFBT
      • Differential Correction Algorithm
      • Differential Correction Principle
      • Differential Correction
      • Differential Corrections
      • Direct Collocation
      • Direct Gravitational Perturbation
      • Direct/Indirect Method
      • Direct Methods
      • Direct Multiple Shooting
      • Direct-Shooting
      • Direct Single Shooting
      • Direct Transcription and Multiple Shooting
      • Direct Transcription
      • Direction Cosine
      • Discrete Euler-Lagrange Equations
      • Discrete Homotopy
      • DMOC
      • Discrete Node
      • Dissipative System
      • Disturbed Manifold
      • Divergent Solution
      • DRO-Lyapunov-DRO Transition Phasing, DLD
      • Discrete Linear Quadratic Regulator
      • Double Pseudo-Range Method
      • Double-Pulse Orbit Transfer
      • DRO Low-energy Capture
      • Dual-Actor Network
      • Dual-Layer Iterative Algorithm
      • Dual-Period Motion
      • Dynamical Channel
      • Dynamical Systems Approach
      • Earth-Moon Manifold
      • Earth-Moon Rotating Frame
      • Earth Non-Spherical Gravity Perturbation
      • Earth oblateness correction
      • Earth-Centered Earth-Fixed Frame
      • Earth-Centered Inertial Frame
      • Eclipse Avoidance Path Constraint
      • Edelbaum's Equation
      • Effective Phase
      • Effective Potential Function
      • EGM2008 Earth Gravitational Model
      • Eigenmotion Method
      • ELERM
      • Elliptic Region
      • Elliptic Restricted Problem
      • Endpoint Homotopy
      • Endpoint Mapping
      • Energy-Descent L₁ Transfer
      • Energy Level
      • Energy-Optimal Control
      • Energy Range
      • Engine Throttle Factor
      • Ephemeris-Based N-Body Model
      • Effective Phases Plane
      • Equilateral Triangle Libration Point
      • Equilibrium Point
      • Equivalent Control
      • Equivalent Libration Point
      • Elliptic Restricted Three-Body Problem
      • Error Dynamics
      • Error Propagation Pattern
      • Earth Restricted Three-Body Problem (ERTBP)
      • Escape Direction
      • Escape Motion
      • Euler-Lagrange Equations
      • Euler Quintic Equation
      • Event Map
      • Exclusion Zone
      • Exosystem
      • Explicit Guidance Law
      • Exponential Divergence Rate
      • Exponential Error Divergence
      • Exponentially Unstable
      • Exterior Stable Manifold
      • Extremal Flow
      • Extreme Terrain Mobility
      • Feedback Linearization
      • Full Ephemeris Restricted 4-Body Problem
      • First-Order Necessary Conditions
      • Fixed-Point Homotopy
      • Fixed-Time Shooting
      • Flight-Path Angle
      • Flight Time Equation
      • Floquet Decomposition
      • Floquet-Lyapunov Theorem
      • Floquet Modal Method
      • Floquet Multiplier
      • Floquet Strategy
      • Flow Function Construction Method
      • Flow Tube
      • Flyby Direction
      • Focal Distance
      • Forbidden Region
      • Force Function
      • Formation Configuration Keeping
      • Formation Fixed Relative to Inertial Frame
      • Formation Stationkeeping
      • Forward-Backward Shooting
      • Forward Lunar Gravity Assist
      • Forward Pass and Backward Sweep
      • Four-Body Problem
      • Fourth-Body Gravitational Perturbation
      • Francis-Byrnes-Isidori Equations
      • Free Transfer
      • Free-variable and Constraint Method
      • Free-variable Constraint
      • Fuel-optimal Control
      • Fuel-optimal Powered Descent
      • Fuel-optimal Control
      • Fuel Optimization
      • Full Force Model
      • Fundamental Solution Set
      • Gauss Planetary Equations
      • Gauss-type Perturbation Equations
      • Geocentric Celestial Reference Frame
      • Generalized ZEM/ZEV Algorithm
      • Generating Function
      • Global Invariant Manifold
      • Gooding Scheme
      • Gooding's Method
      • Gauss Pseudospectral Method, GPM
      • Gravitational Asymmetry
      • Gravitational Potential
      • Gravitational Superhighway
      • Gravity Assist Direction
      • Grid Scan on Poincaré Section
      • Gaussian Smoothing Technique, GST
      • Halo Orbit Computation
      • Hamiltonian Matrix
      • Hamiltonian Normal Form
      • Hamiltonian Reduction
      • Hamiltonian System
      • Hamiltonian
      • Hybrid Differential Dynamic Programming, HDDP
      • Hermite-Simpson Method
      • Heteroclinic Connection
      • Heteroclinic Orbit Transfer (Heteroclinic Orbit Transfer)
      • Heteroclinic Phasing
      • Heterospace System
      • High-Fidelity Dynamics
      • High-fidelity Ephemeris Model
      • High-Fidelity Model
      • Hill Model
      • Hill Problem
      • Hill Region
      • Hill Stability
      • Hill's Problem
      • Hill's Region
      • Low-Thrust Hamiltonian
      • Natural Hamiltonian
      • Hénon f-Family Orbits
      • Hodograph Shaping Method, Velocity Hodograph Method
      • Hohmann-like Transfer
      • Halo Orbit Insertion
      • Homoclinic Connection
      • Homoclinic Phasing
      • Homological Equation
      • Homotopy Continuation Method
      • Homotopy Continuation
      • Homotopy Method (Homotopy Method)
      • Hori Method
      • Horseshoe Map
      • Householder's method
      • Hyperbolic Tangent Smoothing
      • Hybrid Direct/Indirect Optimization Method
      • Hyperbolic Character of Collinear Points
      • Hyperbolic Invariant Manifold Parameters
      • Hyperelliptic Curve
      • Hyperplane Surface of Section
      • Insertion Maneuver, IM
      • Indirect Multi-Stage Formulation, IMF
      • Implicit Costate Transformation
      • Impulse Application Rule
      • Impulse Interval
      • Impulsive Station-Keeping
      • In-plane Amplitude
      • Indirect Collocation
      • Indirect Gravitational Perturbation
      • Indirect Heuristic Method
      • Indirect Methods
      • Indirect Optimization
      • Indirect Phasing
      • Inertial Frame Relative Motion Equations
      • Initial Condition Sensitivity
      • Initial Conjugate Variable Values
      • Initial guess scheme
      • Initial Guess
      • Initialization-Correction-Continuation
      • Inner Frequencies
      • Inner-Loop Outer-Loop Structure
      • Instantaneous Hill's Boundary
      • Integral Invariant
      • Integral Sliding Surface
      • Interior Interval
      • Interior Stable Manifold
      • Intermediate Circular Orbit
      • Intermediate Equations
      • Invariant Manifold Analog
      • Invariant Manifold Attraction
      • Invariant Manifold Connection
      • Invariant Manifold Splicing
      • Invariant Manifold Tube
      • Invariant Manifold (Invariant Manifold)
      • Invariant Torus Manifold
      • Inverse Polynomial Shape Function
      • Interplanetary Superhighway
      • J2 Perturbation
      • J2 term
      • Earth Oblateness Perturbation
      • Jacobi Constant Error Constraint
      • Jacobi Constant Matching
      • Jacobi Constant-Velocity Increment Relationship
      • Jacobi Coordinates
      • Jacobi Decomposition
      • Jacobi Energy
      • Jacobi Integral Monotonicity Criterion
      • Jacobi Constant (Jacobi Integral)
      • Jacobi Constant, JC
      • Jump Condition
      • KAM Theory
      • KAM Tori
      • KAM Torus
      • KAM Theorem
      • Kozai Method
      • Kustaanheimo-Stiefel Transformation
      • KSG Integrator
      • Lambert's Three-Body Problem, L3BP
      • Triangular Libration Points
      • L4
      • L5
      • Lagrange Coefficients
      • Lagrange-d'Alembert Principle
      • Lagrange-Jacobi Identity
      • Lagrange Relaxation
      • Lagrange Stability
      • Lambert Guidance Routine
      • Lambert Guidance
      • Lambert Orbit Maneuver
      • Lambert's Theorem
      • Lambert's Time-of-Flight Theorem
      • Launch Velocity Error
      • Lawden's Necessary Conditions
      • Lunar Centered Rotating Frame
      • Legendre-Clebsch Condition
      • Low-Energy Transfer Gateway
      • Levi-Civita Transformation
      • Libration Point (Equilibrium Point)
      • Lie Transformation
      • Lindstedt-Poincaré Method
      • Lindstedt-Poincare Method
      • Linear Interpolation Parameterization
      • Linear Quadratic Optimal Control
      • Linear Variational Lambert Problem
      • Lagrangian Relaxation Method
      • Lawden's Necessary Conditions
      • Lobatto IIIA Collocation Method
      • Lobe Dynamics
      • Long-period Motion
      • Loss Function
      • Low-Thrust Forbidden Region
      • Low-Thrust Optimization
      • LP to T_min to CEV Continuation Chain
      • LP165P Lunar Gravitational Model
      • Lunar Synodic Resonance
      • Low-Thrust Periodic Orbit
      • Lunar Eccentricity Perturbation
      • Lunar Flyby-Assisted Plane Change
      • Lunar Flyby
      • Lunar Non-Spherical Gravity Perturbation
      • Lunar Proximity
      • Lunar Solid Tide
      • Lunar Surface Capture Energy
      • m-Bifurcation
      • Maneuvering flyby
      • Manifold Family
      • Manifold Initial Value
      • Manifold Insertion
      • Manifold Interpolation Database
      • Manifold Overlap
      • Manifold Parameter
      • Manifold Positive/Negative Branch
      • Manifold Propagation
      • Manifold Segment
      • Manifold Starting Point
      • Mascon (Mass Concentration)
      • Maslov Index
      • Mass Consumption Rate
      • Mass Leak Technique
      • Mass Leak
      • Massive Exploration
      • Matching Conditions
      • Matrix Differential Riccati Equation
      • Monte Carlo Trajectory Shooting, MCTS
      • Multiple-Shooting Differential Dynamic Programming, MDDP
      • Measurement Jacobian
      • Modified Equinoctial Elements
      • Meyer's Method
      • Microgravity Mobility
      • Minimum Euclidean Norm
      • Minimum-Fuel / Fuel-Optimal
      • Minimum Norm Targeting
      • Minimum-Norm Update
      • Minimum-Time Continuous-Thrust Orbit Transfer
      • Multi-Impulsive Staging Guidance, MISG
      • Mixed Method / Hybrid Method
      • Modified Multiple Shooting
      • Monodromy Matrix
      • Monte Carlo Trajectory Shooting
      • Moser Theorem
      • Moving Point Strategy
      • Multi-arc Optimal Control
      • Multi-arc Trajectory Optimization
      • Multi-Impulse Maneuver
      • Multi-Pulse Transfer
      • Multi-Revolution Solution
      • Multi-shooting Convergence Method
      • Multi-Solution Property of Three-Body Lambert Problem
      • Multicollinearity
      • Multiple-Shooting Differential Correction
      • Multiple Shooting Method
      • Multiple-Shooting
      • Multirevolution Lambert Problem
      • N-Body Dynamics
      • Natural Companion Formation
      • Natural Parameter Continuation
      • Natural surrounding fly
      • Near Resonance Theorem
      • Nearly-Integrable Hamiltonian System
      • Neck Opening Condition
      • Neck Region
      • Nekhorosev Estimates
      • Nekhoroshev Theorem
      • Newton-Bisection Hybrid Switching Detection
      • Newton Continuation Method
      • Newton Homotopy
      • Newton-Raphson Method
      • Normally Hyperbolic Invariant Manifold
      • Node
      • Non-Autonomous System
      • Non-Escape Direction
      • Non-Gaussian Distribution
      • Non-Spherical Gravity Terms
      • Non-Spherical Gravity
      • Non-tangential Injection
      • Nonlinear Regulation
      • Nonlinear Tuning
      • Nonspherical Gravitational Perturbation
      • Nonspherical Perturbation
      • Normal Form Reduction
      • Normal Form
      • NRHO Two-Impulse Phasing
      • Near-Rectilinear Halo Orbit Insertion, NRHOI
      • NSGA II (Non-dominated Sorting Genetic Algorithm II)
      • Nonspherical Lunar Gravity
      • Null Space Vector
      • Null Vector
      • Numerical Continuation Strategy
      • numerical continuation
      • Numerical integration (orbit propagation)
      • Numerical Manifold Approximation Method
      • Objective Function
      • Obliquity of Lunar Orbit to Equatorial Plane
      • Optimal Continuation Strategy, OCS
      • Offset
      • Optimal Multi-Impulse, Opt-MI
      • Optimal Initial Costate Locus
      • Optimal Maneuver Beyond Perilune
      • Orbit Balancing Method
      • Orbit-dynamical Boundary Constraints
      • Orbital Aerobraking Return
      • Orbital Boundary Value Problem
      • Orbital Element Drift
      • Orbital Insertion Direction
      • Optimal Sliding Mode Control, OSMC
      • Parabolic Region
      • Parallel Shooting Method
      • Parallel Shooting
      • Parameter Condition
      • Parameter Vector
      • Patch Point (Splicing Point)
      • Patched Restricted Three-Body Problem
      • Patched Three-Body Approximation
      • Patchpoint
      • Planar Bicircular Restricted Four-Body Problem
      • Planar Bicircular Restricted Four-Body Model
      • Planar Bicircular Restricted Four-Body Problem
      • Phase-Constrained Sequential Cone Program
      • Planar Circular Restricted Three-Body Problem, PCR3BP
      • Planar Circular Restricted Three-Body Problem, PCRTBP
      • Penalty Coefficient
      • Periapsis Poincaré Section
      • Perigee Poincaré Map
      • Perilune Database
      • Perilune Poincaré Map
      • Perilune Poincaré Section
      • Periodic Orbit Family at Triangular Libration Point
      • Permanent Capture
      • Permanent Lunar Capture
      • Perturbational Lambert Problem
      • perturbed gravity assist model
      • Perturbed Lambert Arc
      • Perturbed Lambert Problem
      • Perturbed Lambert's Problem
      • Perturbed Restricted Three-Body Problem
      • Phase Deviation
      • Phase Drift
      • Phase Flow Structure
      • Phase Space Conduit
      • Phase Space
      • Phasing Flyby
      • Piercing Point
      • Percentage of Lambert Solutions per Revolution
      • Partial Normal Form
      • Poincaré-Lindstedt Method
      • Poincaré Map Representation
      • Poincaré Map
      • Poincaré Mapping
      • Poincaré Section
      • Poincaré Map
      • Poincaré Section
      • Poisson Bracket
      • Polyhedral Representation
      • Polynomial Amplitude-Phase Assumption
      • Pontryagin's Maximum Principle
      • Position Offset Compensation
      • Potential Function
      • Powell Hybrid Algorithm
      • Power-Limited Engine
      • Practical Stability Region
      • Preceding Phasing
      • Predictor-Corrector Algorithm
      • Predictor-Corrector Method
      • Primaries
      • Primer Vector Theory
      • Primer Vector
      • principal stretching direction
      • Projection Functional
      • PS Plane
      • PS Section
      • Pseudo-Arclength Continuation
      • Pseudo-inverse Newton Update
      • Pseudo-Manifold
      • Pseudo-potential Function
      • Pseudo-potential
      • Pseudospectral Convex Optimization
      • Pseudospectral Discretization
      • Pseudospectral Method
      • Quasi-Periodic Invariant Tori
      • Qualitative Analysis Method
      • Quasi-random Process for Periodic Orbit Generation
      • Quasilinearization Method
      • θ-r Section Method
      • Restricted Three-Body Problem, R3BP
      • Radiation Pressure Model
      • Real Force Model
      • Receding Phasing
      • Region of Prevalence
      • Relative Center Manifold
      • Relative CR3BP Dynamics
      • Relative Hamiltonian
      • Relative Invariant Manifold
      • Relative Motion
      • Relativistic Correction
      • Relaxation Method
      • Reparameterized bounded solution
      • Resonance Hop
      • Resonance Hopping
      • Resonant Manifold
      • Restricted Four-Body Problem
      • Restricted Region
      • Retrograde-Powered Lunar Gravity Assist
      • Receding Horizon Targeting
      • Riccati Equation
      • Richardson Third-Order Analytical Solution
      • Richardson's Method
      • Robust Lambert Solver
      • Radial-Transverse-Normal Frame, RSW Frame
      • Restricted Three-Body Problem, RTBP
      • Runge-Kutta 7/8 Integrator
      • Saddle Point
      • Saddle-Type Unstable Equilibrium Point
      • Safe Transfer Formation
      • Sampling-Based Reachable Set Approximation Algorithm
      • Spatial Bi-Circular Model, SBCM
      • Sequential Convex Programming, SCP
      • Selenopotential Harmonics
      • Sensitivity Matrix Method
      • Sensitivity Matrix
      • Separatrix
      • Shape-Based Method
      • Shape Method
      • Shooting Constraint
      • Shooting Function
      • Shooting Method
      • Shooting Variable
      • Short-period Motion
      • Single-arc Optimal Control
      • Single-Revolution xz-Plane Crossing Control
      • Single Shooting Method
      • Single-Shooting
      • Single-Step Method
      • Single-Step Prediction Method
      • Singular Arc
      • Station-Keeping
      • Slack Factor
      • Sliding Rule
      • Sphere of Influence, SOI
      • Solar Gravity
      • Solar Phase
      • Solar Radiation Pressure Perturbation
      • Solar Radiation Pressure Station Keeping
      • Solar Sail Artificial Libration Point Orbit
      • Solar Sail Propulsion
      • Solar Synodic Frequency
      • Spacecraft Formation Flying
      • Spatial Distribution Uniqueness
      • Spherical Control Variables
      • Spherical Harmonic Gravity
      • Spherical Harmonic Model
      • Spherical Harmonics
      • Spherical Pendulum
      • Spiral Mode
      • Spiral Region
      • Solar Radiation Pressure
      • Solar Sail Circular Restricted Three-Body Problem
      • Stability Factor
      • Stability Region
      • State Constraint
      • State Jacobian Matrix
      • Station-Keeping
      • Stationarity Condition
      • Sticky Region
      • Stream Function Method
      • Strengthened Legendre-Clebsch Condition
      • State Transition Tensor
      • Sub-Riemannian Structure
      • Subarc
      • Subgradient Method
      • Suboptimal Control
      • Successive Convex Optimization
      • Sun-Earth Manifold
      • Sun-Earth Rotating Frame
      • Sun-Earth+Moon Synodic Coordinate System
      • Surface-to-Mass Ratio
      • Surrogate Model
      • Survival Map
      • Switching Function
      • Switching Surface
      • Symbolic Manipulator
      • Symplectic Geometry
      • Symplectic Transformation
      • Synodic Coordinate System
      • System-to-System Transfer
      • System Translation
      • Syzygy Frame
      • Syzygy Rotating Frame
      • Tangent Circle
      • Tangential Impulsive Maneuver
      • Tangential Thrust Control
      • Target Mode
      • Target Point Strategy
      • Targeting Threshold
      • Thrust-Coast-Thrust Sequence
      • Temporary Capture
      • Time-to-Go
      • The angle between the spacecraft velocity vector and the local horizontal plane. A flight path angle of zero indicates the velocity is tangent to the local horizontal, corresponding to the periapsis (or apoapsis) characteristic. The paper uses flight path angle as the differential correction termination condition: integration halts when the angle reaches zero with a negative derivative, identifying the perilune point for constraint evaluation.
      • The branch of the EML2 Halo orbit stable manifold that extends toward the Moon. Unlike the right-pointing manifold which extends away from the Moon, the left-pointing stable manifold asymptotically approaches the Halo orbit in backward integration and moves along the Earth-Moon line toward the lunar side in forward integration, eventually reaching the Moon's vicinity. It is the key orbital structure for low-energy transfers from lunar orbit to EML2 Halo orbit.
      • Theorem of Image Trajectories
      • Theoretical Minimum Velocity Increment, delta-V min
      • Third-Body Perturbation
      • Third-Order Richardson Expansion
      • three-body Lambert problem
      • Three-Body System Translation
      • Three-Dimensional Restricted Problem
      • Three-Impulse Orbit Insertion
      • Three-Impulse Transfer
      • Throttle Factor
      • Throttle Function
      • Thrust Bound
      • Thrust Continuation Method
      • Thrust Continuation
      • Thrust Direction Angle
      • Thrust Direction Cosines
      • Thrust Homotopy
      • Thrust Steering Angle
      • Two-Impulse Maneuver (TI)
      • Tidal Capture
      • Time of Flight on Manifold
      • Time of Permanence in Ballistic Capture
      • Time-Optimal Control
      • Time-Optimal Transfer
      • Timing Constraint Design
      • Tisserand Relation
      • Two-Level Targeter, TLT
      • Time of Flight
      • Trajectory Optimization with Sparse Optimal Control Software, TOSOCS
      • Two-Point Boundary Value Problem (TPBVP)
      • Target Phase
      • TPhA
      • Trajectory Database
      • Trajectory Splicing Database
      • Transfer Cost
      • Transfer Orbit Family
      • Transfer time equation
      • Transfer Time
      • Transit Gate
      • Transitability
      • Transportation Tube Wall
      • Transversality Condition
      • Transversality Conditions
      • Triangular Libration Point
      • Tube Structure
      • Tube Topology
      • Turning Point
      • Two-Impulse Libration Point Transfer
      • Two-Impulse Rendezvous
      • Two-Layer Guidance and Control
      • Two-Point Method
      • Unscented Kalman Filter
      • Ultra-Close Formation
      • Uncertain Multiple-Revolution Lambert Problem
      • Uncertain Lambert Problem
      • Universal Variable Algorithm
      • Universal Variable Method
      • Unmodelled Acceleration
      • Unperturbed Problem
      • Unstable Component Cancellation
      • Unstable Direction
      • Unstable Mode Cancellation
      • V-infinity Matching
      • ΔV-TOF Pareto Front
      • Variable-Time Shooting
      • Variational Equations
      • Velocity Maximum
      • Velocity Minimum
      • Velocity Wedge
      • Vertical Lyapunov Orbit
      • Vertically Stable Manifold
      • Vertically Unstable Manifold
      • Insertion Impulse
      • Variable Specific Impulse Engine, VSI Engine
      • Total Velocity Impulse
      • Area-to-Mass Ratio
      • Weak Instability
      • Weakly Stable Orbit
      • Weierstrass-Erdmann Corner Conditions
      • Stable Manifold
      • Weak Stability Boundary Ballistic Transfer
      • Weak Stability Boundary
      • Weak Stability Region, WSR
      • Unstable Manifold
      • x-z Plane Crossing Target
      • x-Axis Crossing Control, XAC
      • Zero Radial Velocity Condition
      • Zero Velocity Surface, ZVS
      • Zero-Velocity Surface
      • Zonal Harmonic
      • Zero-Velocity Curve
    • Mission orbits

      • approach phase
      • Axial Resonant Orbit, ARO
      • Radial Amplitude
      • Axial Orbit
      • Out-of-plane Amplitude
      • Ballistic Capture
      • Baseline Trajectory
      • Butterfly Orbit
      • central elliptical arc
      • Circular Orbit Boundary Conditions
      • Cislunar Periodic Orbit
      • Classical Exponential Sinusoid
      • Collision Orbit
      • Connection Arc
      • Control Acceleration
      • Cycler Orbit
      • Departure Time
      • Direct Transfer Trajectory
      • Direct Transfer
      • Distant Retrograde Orbit (DRO)
      • Drift Trajectory
      • Earth-Escape Spiral
      • Earth-Moon Triangular Libration Point Transfer Network
      • Eclipse Avoidance
      • Effective Time of Flight
      • EL1 Orbit
      • Energy-Optimal Spiral
      • Energy-to-Fuel Homotopy Continuation
      • Extended Perilune Rendezvous Method, EPRM
      • Earth-Return Orbit
      • Family Curve of Transfers
      • Far Rendezvous
      • Fast Transfer Trajectory
      • Fixed Point
      • Forward-Moon-Retrograde Flyby in Quadrant II
      • Formation Flight
      • Geocentric Arc
      • Geocentric Segment
      • Gravity Assist / Swingby
      • Grouping of Transfers
      • Halo Orbit
      • Heliocentric Graveyard Orbit
      • Heterogeneous Orbits
      • Heterospace-system Manifold Connection
      • Halo Orbit Insertion
      • Horseshoe Orbit
      • Hybrid Multi-Conic Method
      • Inclination Change
      • Insertion Phase Angle
      • Interior Transfer
      • Initial Periodic Orbit
      • Interplanetary Superhighway, ISP
      • Libration Point / Lagrangian Point
      • Lambert patching method
      • Lambert Problem
      • Three-Impulse Lunar Halo Transfer
      • LGA+WSB Transfer
      • Libration Point Orbit (LPO)
      • Linear Periodic Control
      • Lissajous Orbit
      • LOEWE
      • Long-Path Transfer Orbit
      • Long-Way and Short-Way Solutions
      • Low-Energy Transfer
      • Low-thrust Orbit Transfer
      • Low-Thrust Trajectory
      • Lunar Synodic Resonance, LSR
      • Lyapunov Orbit
      • Maneuver Frequency Optimization
      • Manifold Connection
      • Mildly Unstable
      • Minimum Energy Cislunar Transfer
      • Minimum Energy Trans-lunar Transfer
      • Stable Manifold Insertion
      • Moon-Centered Orbit
      • Minimum Parking Orbit
      • Multi-Body Constellation
      • Nominal Orbit
      • Nominal Transfer
      • Non-Keplerian Orbit
      • Non-Transit Orbit
      • North-South Control
      • Near-Rectilinear Halo Orbit (NRHO)
      • Open-Point Scenario
      • Operational Orbit Library
      • Orbit Chain
      • Orbit Chaining
      • Orbit Maintenance Cost
      • Orbital Stability Index
      • Orthogonal Plane-Crossing Condition
      • P2HO2 Orbit
      • Patched Conic
      • Perigee Geocentric Distance
      • Perigee-Point Scenario
      • Perilune Distance
      • Periodic Orbit Family
      • Periodic Solution
      • Phasing Loop Transfer
      • Pole-Sitter
      • Position-Keeping
      • Prograde in Perigee and Retrograde in Perilune
      • Pseudo-Equinoctial Orbital Elements
      • Quasi-Periodic Orbit, QPO
      • Quasi-Satellite Orbit (QSO)
      • Resonant Orbit, RES
      • Rescue Orbit
      • Resonant Orbit Family
      • Resonant Orbit
      • Perilune Radius
      • Selenocentric Segment
      • Semiminor Axis
      • Super-Geostationary Transfer Orbit
      • Short-Path Transfer Orbit
      • Short-Reach Arrival
      • Special Long-Period Orbit, SLPO
      • SMART-like Transfer
      • Smoothed Trajectory
      • Single-shooting Differential Corrector
      • Storage Orbit
      • Tadpole Orbit
      • Tangential Insertion
      • Tangential Intersection
      • Tangential
      • Orbit Phase
      • Touring Cislunar Periodic Orbit, TCPO
      • The distance from the Moon's center to the closest point of a transfer trajectory or invariant manifold
      • The location on a Halo orbit where the spacecraft transitions from the transfer trajectory onto the periodic orbit. The phase angle of the injection point determines the required velocity increment. For zero-cost transfers, the injection impulse is zero; for perturbed transfers, small impulses are typically needed (0-8 m/s in this paper). The paper divides the Halo orbit into 360 equally-spaced nodes, each a potential injection point.
      • Three-Body Periodic Orbit
      • Thrust-Magnitude Continuation
      • Minimum-Thrust Trajectory
      • Trajectory Section Width
      • Transfer Family
      • Two-maneuver transfer design
      • Two-Phase Transfer
      • Unpowered Lunar Gravity Assist, Unpowered LGA
      • Lunar DRO Insertion Delta-V
      • Vertical Orbit
      • Manifold Insertion
      • Weak Stability Boundary Transfer Trajectory
      • Weak Stability Region Transfer
      • x₀ Value
      • Zero-Cost Transfer Trajectory
      • z-direction Motion Amplitude
    • Navigation & systems

      • Absolute Navigation
      • Autonomous Orbit Determination
      • B-Plane Parameters
      • Barycentric Inertial Frame
      • Barycentric Rotating Frame
      • Batch Least-Squares Differential Correction
      • Bidirectional Inter-Satellite Ranging
      • Combined Autonomous Orbit Determination, CAOD
      • Cislunar Space Satellite Navigation System
      • Close-Range Rendezvous
      • Coverage Blind Spot
      • deep space navigation constellation
      • Deficient Rank
      • Differential Correction
      • DRO GNSS Shadowing by Moon
      • Dual-Layer Inter-Satellite Link
      • Dual Navigation Satellite Scheme
      • Earth-Moon Barycenter Rotating Frame
      • Extended Kalman Filter
      • Engine Limitation
      • Extended Constellation
      • GNSS Sidelobe Signal Navigation
      • Grid Division Method
      • Halo Orbit Rendezvous
      • High-Precision Cislunar Space-Time Benchmark
      • Identifiability Information Matrix
      • Inter-Satellite Ranging
      • Iterative Guidance
      • Linked Autonomous Orbit Determination, LAOD
      • Lunar Global Navigation Satellite System
      • Lunar Global Positioning System, LGPS
      • Liaison Navigation
      • Libration Point Navigation Constellation
      • Libration Point Navigation
      • Linearization Method
      • LNSS-A
      • LPO Constellation
      • Lunar Global Positioning Satellite Constellation
      • Lunar High-Latitude Region
      • Lyapunov Optimal Feedback Guidance
      • Multiple Solutions Phenomenon
      • Navigation Constellation
      • Navigation Update Interval
      • Normal Matrix
      • Northern and Southern NRHO Families
      • NRHO Rendezvous and Docking
      • Optimal Control Based Estimator, OCBE
      • Orbital Amplitude
      • Orbital Rendezvous
      • Phase-Based Deployment Strategy
      • Phasing Maneuver
      • Primary Celestial Body
      • Propulsion Error
      • Rank Deficiency Problem
      • Reference Orbit
      • Relative Trajectory Following
      • Sub-Optimal Feedback Control
      • Starlight Angle
      • Time Synchronization Accuracy
      • Transfer Cost Heat Map
      • Two-Step Optimization Algorithm
      • Unscented OCBE, U-OCBE
      • Unscented Transformation, UT
      • Virtual Trajectory
      • Wait Time
    • Astronomy & observation

      • Access Time
      • Cooperative Agent, CA
      • Cislunar Domain Awareness
      • Cislunar Libration Point Constellation
      • Cislunar Navigation Constellation
      • DRO Capture Projection Surface
      • Dynamic Demand
      • Dynamics-Based Statistical Orbit Determination
      • Earth-Atmosphere Off-Axis Angle
      • Gravitational Delay
      • GRGM1200A Lunar Gravity Field Model
      • GRAIL Gravity Field Model
      • Kordylewski Cloud
      • Kordylewski Clouds
      • Lunar Exclusion Angle
      • Lunar Impact
      • Lunar Occultation Avoidance
      • Lunar Surface Coverage Assessment
      • Observation Constellation
      • Relay Observation
      • Solar Suppression Angle
      • Solar Synodic Period
      • Valuable Region
      • Initial Solar Phase Angle

Trajectory Splicing Database

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A pre-computed database storing various typical trajectory segments (Earth departure, LGA, invariant manifold, orbit insertion, etc.) that enables rapid generation of feasible transfer solutions by splicing segments, avoiding optimization from scratch.

References

  • Shi et al. (2025)
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Last Updated: 8/1/26, 12:08 AM
Contributors: ouyangjiahong
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