Glossary
========

This glossary defines key terms used in HITEN and dynamical systems analysis.

A
-

**Attractor**
    A set of points in phase space that trajectories approach as time goes to infinity.

B
-

**Bifurcation**
    A qualitative change in the behavior of a dynamical system as a parameter is varied.

**Bifurcation Point**
    A parameter value at which a bifurcation occurs.

**Birkhoff Normal Form**
    A canonical form for Hamiltonian systems near equilibrium points.

C
-

**Center Manifold**
    A manifold of equilibrium points that contains all the bounded solutions near the equilibrium.

**Circular Restricted Three-Body Problem (CR3BP)**
    A simplified model of three-body dynamics where one body has negligible mass and the other two bodies move in circular orbits.

**Collinear Points**
    The L1, L2, and L3 Lagrange points, which lie on the line connecting the two primary bodies.

D
-

**Dynamical System**
    A system whose state evolves over time according to a set of differential equations.

**Dynamical System Theory**
    The mathematical study of dynamical systems and their properties.

E
-

**Equilibrium Point**
    A point in phase space where the time derivative of the state is zero.

F
-

**Family of Orbits**
    A continuous set of orbits parameterized by one or more parameters.

**First Integral**
    A function that remains constant along trajectories of a dynamical system.

**Fourier Series**
    A representation of a periodic function as a sum of sinusoidal functions.

G
-

**Gravitational Parameter**
    The product of the gravitational constant and the mass of a celestial body.

H
-

**Hamiltonian**
    A function that describes the total energy of a dynamical system in terms of position and momentum variables.

**Hamiltonian System**
    A dynamical system whose equations of motion can be derived from a Hamiltonian function.

**Halo Orbit**
    A three-dimensional periodic orbit around a Lagrange point.

I
-

**Invariant Manifold**
    A manifold that is invariant under the flow of a dynamical system.

**Island of Stability**
    A region in phase space where trajectories remain bounded for long times.

J
-

**Jacobi Constant**
    A conserved quantity in the CR3BP that plays a role similar to energy.

**Jacobi Integral**
    Another name for the Jacobi constant.

L
-

**Lagrange Points**
    Five equilibrium points in the CR3BP where the gravitational and centrifugal forces balance.

**Libration**
    Oscillatory motion around an equilibrium point.

**Libration Points**
    Another name for Lagrange points.

M
-

**Mass Parameter**
    The ratio of the smaller primary mass to the total mass in the CR3BP.

**Monodromy Matrix**
    A matrix that describes how small perturbations evolve over one period of a periodic orbit.

N
-

**Normal Form**
    A simplified form of a dynamical system near an equilibrium point or periodic orbit.

**Normal Mode**
    A mode of oscillation in a linearized system.

O
-

**Orbit**
    The path followed by a particle in phase space.

**Orbital Period**
    The time required for one complete orbit.

P
-

**Periodic Orbit**
    An orbit that returns to its initial state after a finite time.

**Phase Space**
    The space of all possible states of a dynamical system.

**Poincare Map**
    A map that describes how trajectories intersect a surface of section.

**Poincare Section**
    A surface in phase space used to study the dynamics of a system.

**Poisson Bracket**
    A binary operation on functions in phase space that is fundamental to Hamiltonian mechanics.

R
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**Restricted Three-Body Problem**
    A three-body problem where one body has negligible mass.

**Rotating Frame**
    A coordinate system that rotates with the primary bodies.

S
-

**Stable Manifold**
    The set of points that approach an equilibrium point or periodic orbit as time goes to infinity.

**Surface of Section**
    Another name for Poincare section.

**Symplectic**
    A property of transformations that preserve the symplectic structure of phase space.

T
-

**Triangular Points**
    The L4 and L5 Lagrange points, which form equilateral triangles with the two primary bodies.

**Trajectory**
    The path followed by a particle in phase space over time.

U
-

**Unstable Manifold**
    The set of points that approach an equilibrium point or periodic orbit as time goes to negative infinity.

V
-

**Variational Equations**
    Linearized equations that describe how small perturbations evolve in a dynamical system.

W
-

**Weak Stability Boundary**
    A region in phase space where trajectories are weakly stable.

Z
-

**Zero-Velocity Surface**
    A surface in configuration space where the velocity is zero for a given value of the Jacobi constant.