Velocity: Difference between revisions
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Eric Lengyel (talk | contribs) (Created page with "The velocity $$\mathbf u$$ of a body in spacetime is given by :$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ , where $$\mathbf r$$ is the body's position and $$\tau$$ is proper time. == See Also == * Position * Momentum") |
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:$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ , | :$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ , | ||
where $$\mathbf r$$ is the body's [[position]] and $$\tau$$ is proper time. | where $$\mathbf r$$ is the body's [[position]] and $$\tau$$ is proper time. The velocity $$\mathbf u$$ has units of length / time. | ||
== See Also == | == See Also == | ||
Latest revision as of 01:24, 20 November 2024
The velocity $$\mathbf u$$ of a body in spacetime is given by
- $$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,
where $$\mathbf r$$ is the body's position and $$\tau$$ is proper time. The velocity $$\mathbf u$$ has units of length / time.