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The location of a particle in three-dimensional space requires three position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. If the time evolution of the system is deterministic, where the state at one instant uniquely determines its past and future position and velocity as a function of time, such a system has six degrees of freedom. If the motion of the particle is constrained to a lower number of dimensions – for example, the particle must move along a wire or on a fixed surface – then the system has fewer than six degrees of freedom. On the other hand, a system with an extended object that can rotate or vibrate can have more than six degrees of freedom.
The location of a particle in three-dimensional space requires three position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. If the time evolution of the system is deterministic, where the state at one instant uniquely determines its past and future position and velocity as a function of time, such a system has six degrees of freedom. If the motion of the particle is constrained to a lower number of dimensions – for example, the particle must move along a wire or on a fixed surface – then the system has fewer than six degrees of freedom. On the other hand, a system with an extended object that can rotate or vibrate can have more than six degrees of freedom.
一个粒子在三维空间中的位置需要三个位置坐标进行标识。类似地，我们也可以根据三个速度分量来描述粒子运动的方向和速度，每个速度分量都参考该空间的三个维度。如果系统的时间演变是确定的，那么其中某个瞬间以及其过去和未来瞬间的位置和速度，均可以被该瞬间的状态确定为时间函数，相应地，这种系统具有六个自由度。如果将粒子的运动轨迹限制在更小的维度里面，例如，粒子必须沿着电线或在固定的表面上移动，那么系统的自由度则小于6。另一方面，如果一个系统带有可旋转或振动的扩展对象，那么它将具有六个以上的自由度。