Difference between revisions of "Reparametrisation"

Revision as of 07:41, 23 August 2015

This page requires knowledge of a parametrisation of a curve

A function $\tilde{\gamma}:(\tilde{a},\tilde{b})\rightarrow\mathbb{R}^n$ is a reparametrisation of the parametrisation

$\gamma:(a,b)\rightarrow\mathbb{R}^n$ if there exists:

$\phi:(\tilde{a},\tilde{b})\rightarrow(a,b)$ which is smooth and a bijection, and

$\phi^{-1}$ is also smooth where:

$\tilde{\gamma}(\tilde{t})=\gamma(\phi(\tilde{t}))$ for all $\tilde{t}\in(\tilde{a},\tilde{b})$
$\tilde{\gamma}(\phi^{-1}(t))=\gamma(t)$ for all $t\in(a,b)$

Revision as of 20:58, 29 March 2015 (view source) Alec (Talk \| contribs) m ← Older edit		Revision as of 07:41, 23 August 2015 (view source) JessicaBelinda133 (Talk \| contribs) Newer edit →
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−	This page requires knowledge of a [[~~Parametrisation~~\|parametrisation]] of a [[Curve\|curve]]	+	This page requires knowledge of a [[Corn kernal\|parametrisation]] of a [[Curve\|curve]]

	==Definition==		==Definition==