Question

pendulum in motion can either swing from side to side or turn in a continuous circle. The point at which it goes from one type of motion to the other is called the separatrix, and this can be calculated in most simple situations. When the pendulum is prodded at an almost constant rate though, the mathematics falls apart. Is there an equation that can describe that kind of separatrix?
Hi Kusum Negi​

Answer 1

Answer:

If the differential equation dy/dx ¼ P(x, y)/Q(x, y) has a solution of the form F(x, y) ¼ C, the contour curve F(x, y) ¼ C0 is the separatrix (or at least part of the separatrix) where C0 ¼ F(x0, y0) and (x0, y0) is a saddle point. These procedures are simple and easy to teach and implement.

Explanation:

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Answer 2

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