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Thread: Reparametrization and vector fields

  1. #1
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    Reparametrization and vector fields

    Let $\displaystyle Y$ be a vector field on a curve $\displaystyle \alpha$. If $\displaystyle \alpha (h)$ is a reparametrization of $\displaystyle \alpha$, show that the reparametrization $\displaystyle Y(h)$ is a vector field on $\displaystyle \alpha (h)$.

    I'm a bit stuck and would appreciate some help.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Zennie View Post
    Let $\displaystyle Y$ be a vector field on a curve $\displaystyle \alpha$. If $\displaystyle \alpha (h)$ is a reparametrization of $\displaystyle \alpha$, show that the reparametrization $\displaystyle Y(h)$ is a vector field on $\displaystyle \alpha (h)$.
    I don't know which is the problem. If $\displaystyle h$ is a reparametrization of $\displaystyle \alpha$ then, there exists $\displaystyle Y\circ \alpha \circ h$ .
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