next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |
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: . |
next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |
© Robert FERRÉOL 2017