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In particular one can find a distance that the center of the coin passes as the coin makes one complete revolution: $$\Delta...

yes My solution is as follows. Introduce a frame ##OXYZ## such that the axis ##OZ## is directed upwards. The sides of the groove a the...

See Chapter 3 Section 6: F. Riesz' Representation Theorem and Corollary 1 therein. In the case of ##\mathbb{C}## the isomorphism between...

On the other hand consider a real Hilbert space ##F## of sequences ##x=(x_1,x_2,\ldots)## with inner product $$(x,y)_F=\sum_{k=1}^\infty...

Hope you are speaking about Hilbert spaces. If it is so you should separate two cases: a Hilbert space over ##\mathbb{R}## and over...

it is not simple harmonic motion

it is hard to answer questions that contain incorrect prerequisites in their formulations :)

the equation of motion has already been written what else do you want ?

Here I would like to draw colleagues attention to a class of problems that are simple from physics viewpoint but have pure geometric...

Actually it is a pendulum. The equations of motion are the same as ones for the pendulum.

You ask irrelevant question. Analyze formulas and make sure that ##as(t)\in [0,\pi]## for all ##t\ge 0##; ##s(t)## is a periodic function

the 2nd Newton is ##m\ddot s=F\cos(as)## and ##s(0)=0,\quad \dot s(0)=0##. multiply both sides of the equation by ##\dot s##: ##m\ddot...

picture is needed

A mechanical system consists of rigid bodies and particles. Sometimes we a priori know something about motion of some components of the...