softmatter:Newton's equations of motion

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Newton's laws of motion can be summarized as:

  • 1. A body continues to move in a straight line unless there's a force acting on it.
  • 2. Force equals the time rate of change of momentum.

m\mathbf{\ddot{r}}_i = \mathbf{\dot{p}}_i = \mathbf{F}_i = -\nabla U_i

\mathbf{r} \equiv x\mathbf{\hat{x}}+ y\mathbf{\hat{y}} + z\mathbf{\hat{z}}

  • 3. To every action there is an equal and opposite reaction.

\mathbf{F}_{ij} = -\mathbf{F}_{ji}

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