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Let $P$ be a particle whose position vector at time $t$ is $\mathbf r$.
Let a force applied to $P$ be represented by the vector $\mathbf F$.
Suppose that, during the time interval $\delta t$, $P$ moves from $\mathbf r$ to $\mathbf r + \delta \mathbf r$.
The work done by $\mathbf F$ during $\delta t$ is defined to be:
- $\delta W = \mathbf F \cdot \delta \mathbf r$
where $\cdot$ denotes the dot product.
- 1961: D.S. Jones: Electrical & Mechanical Oscillations ... (previous) ... (next): Chapter $1$: Equilibrium: $1.1$ Introduction
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (next): Chapter $1$ Vector Analysis $1.3$ Scalar or Dot Product