Well posed formulations of holonomic mechanical system dynamics and design sensitivity analysis

• Edward J. Haug ^[1]
  1. [1] University of Iowa

     University of Iowa

     City of Iowa City, Estados Unidos

     
• Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 48, Nº. 1, 2020, págs. 111-121
• Idioma: inglés
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• Resumen

  • Manifold theoretic ordinary differential equations of motion for holonomic mechanical systems that depend on problem data, or design variables, are shown to be well posed; i.e., they have a unique solution that depends continuously on problem data. It is proved that these differential equations are equivalent to the d’Alembert variational formulation and the index 3 Lagrange multiplier formulation of differential-algebraic equations of motion, which are also shown to be well posed. These results provide a foundation for dynamic system design sensitivity analysis, which requires differentiability of solutions of the equations of motion with respect to design variables.