Consider a simple 1-D system consisting of two identical massive particles (with mass ). One is fixed at the origin, and the other is free to move and is located a distance from the origin.
If each particle only experiences the gravity force from the other particle, the differential equation describing the moving particle's position is:
We can derive this expression by formulating the behavior of the system in terms of Lagrangian mechanics . In that case, which part of the Euler equation does the term correspond to?
Notes: The dot notation denotes time-differentiation. The term represents the Lagrangian of the system. The term is the universal gravitational constant.
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