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ISOENERGY CURVE OF THE PENDULUM

Other names: Horus eyes, almond eyes, cat eyes, etc... |

Cartesian equation: ,
or , with .
Special case (blue curve) k = 1: double
sinusoid: . |

Since the total energy of the simple
pendulum of mass *m* and length *l* forming an angle
with the vertical is equal to ,
the equation of the isoenergy curve is .
They are the curves above, with .

The two blue sinusoids above are the limit between the
oscillating pendulum (closed internal curves) and the turning pendulum
(external curves).

See on this
page a superb animation tracing the isoenergy curves, including the
case of the motion with friction.

With , we get a cylindrical winding of this curves: they are bicylindrics with equation: . |

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© Robert FERRÉOL 2017