Details

The dynamics of the system can be modeled using Lagrangian mechanics.

Let be the position of mass in 3D. The total kinetic energy due to the motion of the masses is:

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Define as the graph of 20 mass-to-mass spring linkages. The total potential energy due to deformation of all springs is:

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Hence the Lagrangian expression is:

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The total negative work due to spring damping can be written as a Rayleigh dissipative function:

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Hence the equations of motion for the masses are given by the Euler–Lagrange equations:

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