Discover published sets by community

A stable orbit is one where nearby trajectories remain close to the orbit over time, implying future behavior remains predictable.

An unstable orbit is such that nearby trajectories diverge away from the orbit over time, making future behavior increasingly unpredictable.

A heteroclinic orbit connects different critical points or equilibria in phase space. Its presence indicates the system's transitions between different states.

A homoclinic orbit connects a critical point with itself in phase space, potentially indicating complex, chaotic behavior in dynamical systems.

A periodic orbit repeats its path in phase space after a fixed period, showing a regular, cyclic behavior in a dynamical system.

A quasi-periodic orbit is characterized by motion on a torus in phase space, with frequencies that are incommensurate, leading to non-repeating trajectories that fill the torus.

A chaotic orbit displays sensitive dependence on initial conditions, leading to unpredictability and a trajectory that appears random in a deterministic system.

A Lyapunov orbit exists near equilibrium points in the vicinity of gravitational bodies, where the gravitational pull and centrifugal force balance each other.

A transfer orbit is used by spacecraft to move between two different orbits, often described by the Hohmann transfer orbit which is an energy-efficient path.