Epilogue

• Application to contact mechanics:
  • problem: system changes number of degrees of freedom
  • physical cause: use of rigid bodies
  • solution: add elasticity c and damping d
  • choose d carefully
  • new problem: (very) stiff system
• Better way: Dialectic Mechanics (Zimmer, Oldemeyer 2023):
  • split forces into elastic and kinetic part
  • introduce slow kinetic velocity v_ki and fast elastic velocity v_el
  • introduce smoothing time scale T_D and low-pass filter v_ki
    • 
    • in steady-state v_ki = v_el
  • implementation in Modelica
    • adapt connector
    • distribute equations to components (mass, joints)
    • → reproduces equilibrium dynamics
    • → damps high-frequency behaviour
• Beware: It's often not simple !