Double spherical pendulum interactions #shorts

Double spherical pendulum interacting with two soft sphere particles inside a sphere, demonstrating exchange of energies between the objects. All interactions are perfectly elastic and soft collisions. All masses but the rods are set to 1.

The double spherical pendulum was expressed explicitly as a Hamiltonian system with excessive Cartesian coordinates, allowing for efficient simulations using Hamilton's equations.

The interaction potential of particles and the spherical boundary are bump functions. A bump function is a special type of function which has continuous derivatives of all orders and is compactly supported. This allows for simulating this system with n particles in O(n log(n)) without waiving symplectic properties.

This system was simulated using high order explicit symplectic integrators, preserving the energy of the system.
#shorts

[antonhengst]

HOW

HOW IS THERE A SYMPLECTIC SOLUTION TO THIS