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词汇 Uniformly accelerated motion
分类 英语词汇 英语翻译词典
释义

Uniformly accelerated motion

中文百科

运动方程 Equations of motion

（重定向自Uniformly accelerated motion）

运动方程是刻划系统运动的物理参量所满足的方程或方程组。它们以这些参量对于时间的微分方程形式出现。

  • 牛顿力学中的运动方程（牛顿第二定律）：
{\mathbf{F}} = m{\mathbf{a}}
  • 拉格朗日力学中的运动方程（拉格朗日方程）：
{d\over dt}{\partial{L}\over \partial{\dot{q_i}}} - {\partial{L}\over \partial q_i} =0
  • 哈密顿力学中的运动方程（哈密顿正则方程）：
{\partial H \over \partial q_j} = - \dot{p}_j, \qquad {\partial H \over \partial p_j} = \dot{q}_j, \qquad
  • 量子力学中的运动方程（薛定谔方程）：
i\hbar \frac{\partial \Psi(\vec{x},t)}{\partial t}=\hat{H}\Psi(\vec{x},t)
英语百科

Equations of motion 运动方程

（重定向自Uniformly accelerated motion）
Kinematic quantities of a classical particle of mass m: position r, velocity v, acceleration a.
Trajectory of a particle with initial position vector r0 and velocity v0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t.
Position vector r, always points radially from the origin.Velocity vector v, always tangent to the path of motion.Acceleration vector a, not parallel to the radial motion but offset by the angular and Coriolis accelerations, nor tangent to the path but offset by the centripetal and radial accelerations.Kinematic vectors in plane polar coordinates. Notice the setup is not restricted to 2D space, but a plane in any higher dimension.

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behaviour of a physical system as a set of mathematical functions in terms of dynamic variables: normally spatial coordinates and time are used, but others are also possible, such as momentum components and time. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions to the differential equations describing the motion of the dynamics.
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