Concept

List of periodic functions

This is a list of some well-known periodic functions. The constant function _ () = , where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions. All trigonometric functions listed have period , unless otherwise stated. For the following trigonometric functions: Un is the nth up/down number, Bn is the nth Bernoulli number in Jacobi elliptic functions, The following functions have period and take as their argument. The symbol is the floor function of and is the sign function.

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https://en.wikipedia.org/wiki/List_of_periodic_functions

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The curve generated by a point M of a circle of radius R′ that rolls without slipping inside a larger circle of radius R is a hypocycloid.

Show that the condition of rolling without slipping is given by (R−u2006R′)ϕ̇+u2006R′ψ̇u2004=u20040xa0, where ϕ is the angle of rotation of the centre of the small circle with respect to the large circle and ψ is the intrinsic angle of rotation of the small circle.
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