A particle of mass $m$ is on top of a frictionless hemisphere centered at the origin with radius $R$. It starts sliding down the hemisphere. Set up the Lagrange equations of the first kind and dete...

Graphing it out, it looks like a normal hemisphere cut in half at the Y axis. When we learned how to infer the values of φ and θ for a parameterized sphere in class, we were told that generally φ is the …

Parameterizing the upper hemisphere of a sphere with an upward pointing normal Ask Question Asked 14 years, 7 months ago Modified 14 years, 7 months ago

if a sphere is of the equation $r^2 = x^2 + y ^2 +z ^2$ and we want to find a hemisphere does that just involve setting a limit to be half of the radius ? For example ...

Nov 7, 2015 · I believe there are three outer normal vectors, but the equation you wrote down is for Green's theorem, and it's not clear what you want to do.

Aug 17, 2018 · Is there an equation that could represent any latitudinal line that lies along the surface of the hemisphere? I want to be able to have an equation that could describe the curve that runs along …

Sep 5, 2020 · A hemisphere is obtained by restricting $\theta$ to $ [0,\frac {\pi} {2}]$. Here is a vizualization from Wikipedia: Coming up with this quickly is not something you're supposed to do in …

Dec 20, 2013 · But as I understand Stokes' theorem which relates a surface integral to the line integral of its boundary, the normal vector of the surface to integrate must be a unit vector, but the textbook …

Dec 7, 2024 · I'm attempting to derive the centre of mass of a uniform hemispherical shell by considering it as a series of circular strips of width dx. Like a solid of revolution but with circular strips rather...

Sep 29, 2019 · Equation of non-axis-aligned ellipse resulting from hemisphere projected circle Ask Question Asked 5 years, 11 months ago Modified 5 years, 11 months ago