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Results tagged with newtonian-mechanics
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user 311583
Newtonian mechanics discusses the movement of classical bodies under the influence of forces by applying Newton’s three laws. For more general concepts, use [classical-mechanics]. For Newton’s description of gravity, use [newtonian-gravity].
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Galilean's principle implies independence of time and dependence on relative distance
Suppose a system of particles $q_1,\ldots,q_N$ of masses $m_1,\ldots,m_N$ that follow the equations of motion
$$m_j\ddot{q}_j=f_j(q_k,\dot{q}_k)$$
in an inertial frame and satisfy the Galilean princi …
- 101
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Accepted
Galilean's principle implies independence of time and dependence on relative distance
Take the Galilean's transformation $(q_{j},t)\mapsto(q_{j},t+t_{0})$ then, by the principle of relativity
$$f_{j}(q_{k},\dot{q}_{k},t+t_{0})=f_{j}(q_{k},\dot{q}_{k},t).$$
Since $t_{0}\in\mathbb{R}$ is …
- 101