State
In classical mechanics, the state of a system is the complete set of information needed to predict its future evolution, assuming the laws of motion are known.
For a single particle moving in one dimension, the state is usually given by two numbers:
- its position, usually written as \(x\)
- its velocity, usually written as \(v\), or equivalently its momentum \(p = mv\)
Knowing only the position is not enough. A particle at the same point can be moving left, moving right, or momentarily at rest. To know what happens next, we need both where it is and how it is moving.
For a particle moving in three dimensions, the state requires three position coordinates and three velocity or momentum components:
For a system with many particles, the state consists of the positions and velocities, or positions and momenta, of every particle. This collection of possible states is called the state space or phase space.
The central idea is simple: once the present state is known, the laws of classical mechanics determine the future state.