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A Mathematics enthusiast.

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Jul
21
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@Winther : Agree it seems obvious, but I do need the "make the argument precice enough" with mathematically complete proof. I am not only interested in the result but also the way we prove it here, as I want to do more with... If its so obvious I still not able to prove it and that puzzles me!
Jul
16
awarded  Notable Question
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@ja72 : I have added a detail that how curve $C$ is asymptotic to a straight line $(a,s)$ in arc length parametrization, where $a$ is a fixed constant.
Jul
12
revised Question on Moment of inertia about center of mass of a smooth plane curve.
added 64 characters in body
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
$s\to\infty$ means both are of infinite length.
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@ja72 : Both curves are of infinite length. Thats what i mean by asymptotic and approaching as $s\to\infty$
Jul
12
revised Question on Moment of inertia about center of mass of a smooth plane curve.
added clarity
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@ja72 : I dont understand why you are goint to two dimensions, the curve is just a uniform string. There is no question of area here.
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@ja72 : dont change question for sake of units. This inst physics, just math definitions. In any case for physical meaning, the curve is of uniform linear mass density equal to 1.
Jul
12
revised Question on Moment of inertia about center of mass of a smooth plane curve.
added 28 characters in body
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@DavidH : In case you were wondering, Altogether elimination of CoM is not possible$(X_{cm},Y_{cm})$ is the center of mass of the segment of curve we are considering, and not a fixed constant for all segments of the curve. It changes when we change when we move from one segment of the curve to another segment of the curve. Ofcourse it also changes when we move to another curve.
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
@DavidH : I know. The CoM can safely assumed to be origin without any loss to the problem. Infact thats what RobJohn did in his answer : math.stackexchange.com/a/618993/2987
Jul
12
comment Question on Moment of inertia about center of mass of a smooth plane curve.
mathoverflow.net/a/175862/14414
Jul
12
asked Question on Moment of inertia about center of mass of a smooth plane curve.
Jul
2
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Jul
2
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Jul
2
asked relation between moment of inertia about center of mass and curvature energy for a smooth plane curve of finite fixed length.
Jun
24
awarded  Notable Question
May
22
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Apr
6
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