“equation of motion”的概念、定义、翻译、参考文献-科学参考

equation of motion

Physics

Any of four equations that apply to bodies moving linearly with uniform acceleration (a). The equations, which relate distance covered (s) to the time taken (t), are:

$\begin{array}{l} v = u + a t \\ s = (u + v) t / 2 \\ s = u t + a t^{2} / 2 \\ v^{2} = u^{2} + 2 a s \end{array}$

where u is the initial velocity of the body and v is its final velocity.

Mathematics

An equation, based on the second of Newton’s laws of motion, that governs the motion of a particle. In vector form, the equation is $m \ddot{r} = F$ , where F is the total force acting on the particle of mass m. In Cartesian coordinates, this is equivalent to the three differential equations $m \ddot{x} = F_{1}$ , $m \ddot{y} = F_{2}$ and $m \ddot{z} = F_{3}$ , where F = F₁i + F₂j + F₃k. In cylindrical polar coordinates, taken here to be (r,θ‎,z), it is equivalent to $m (\ddot{r} - r {\dot{θ}}^{2}) = F_{1}$ , $\frac{m}{2} \frac{d}{d t} (r^{2} \dot{θ}) = F_{2}$ , and $m \ddot{z} = F_{3}$ , where now F = F₁e_r + F₂e_θ‎ + F₃k, and e_r = i cosθ‎ + j sinθ‎ and e_θ‎ = −i sinθ‎ + j cosθ‎ (see radial and transverse components).

单词	equation of motion
释义	equation of motion Physics Any of four equations that apply to bodies moving linearly with uniform acceleration (a). The equations, which relate distance covered (s) to the time taken (t), are: $\begin{array}{l} v = u + a t \\ s = (u + v) t / 2 \\ s = u t + a t^{2} / 2 \\ v^{2} = u^{2} + 2 a s \end{array}$ where u is the initial velocity of the body and v is its final velocity. Mathematics An equation, based on the second of Newton’s laws of motion, that governs the motion of a particle. In vector form, the equation is $m \ddot{r} = F$ , where F is the total force acting on the particle of mass m. In Cartesian coordinates, this is equivalent to the three differential equations $m \ddot{x} = F_{1}$ , $m \ddot{y} = F_{2}$ and $m \ddot{z} = F_{3}$ , where F = F₁i + F₂j + F₃k. In cylindrical polar coordinates, taken here to be (r,θ‎,z), it is equivalent to $m (\ddot{r} - r {\dot{θ}}^{2}) = F_{1}$ , $\frac{m}{2} \frac{d}{d t} (r^{2} \dot{θ}) = F_{2}$ , and $m \ddot{z} = F_{3}$ , where now F = F₁e_r + F₂e_θ‎ + F₃k, and e_r = i cosθ‎ + j sinθ‎ and e_θ‎ = −i sinθ‎ + j cosθ‎ (see radial and transverse components).
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