Equation of motion from the potential energy ↩

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created: 2022-07-08 22:18:48
modified: 2022-07-08 22:25:40

We can get an equation of motion for a 1D particle if its potential energy and its initial kinetic energy is known:

Derivation

Let's start from the conservation of energy, where there is a constant such that:

Where is the kinetic energy and is the potential energy.

Then we can get this just from simple rearrangement:

And by integration, we get:

So with a given , we can find , because determines the motion of the particle.