1. slevvio

    geodesic is parametrised by a constant multiple of arc length

    Let S\in \mathbb{R}^3 be a regular surface, and \gamma: I \rightarrow S a geodesic, where I is an open interval in \mathbb{R}. We have that \frac{d}{dt}|\gamma ' (t) | = 0 \implies |\gamma '(t)| = c, a constant , i.e. \frac{ds}{dt} = | \gamma' (t) | = c ..................(1) where...
  2. N

    Parametrised Curve Problem

    Would appreciate some help with this one please.
  3. T

    Parametrised by arc length

    Parametrised curves Suppose that \alpha(t) is the parametrised curve given by \alpha(t) = \left(\begin{array}{c}sin^2(t)\\sin(t)cos(t)\end{array}\right) for 0 \leq t \leq \pi. Show that \alpha(t) is parametrised by arc length. Find the length of \alpha(t). Find the normal vector to...