Principles of Analytical System DynamicsMechanical engineering, an engineering discipline borne of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound is sues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consult ing editors on the advisory board, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the next page of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, en ergetics, mechanics of materials, processing, thermal science, and tribology. Fred Leckie, our consulting editor for applied mechanics and I are pleased to present this volume in the Series: Principles of Analytical System Dy namics, by Richard A. Layton. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our read ers with topical monographs as well as graduate texts in a wide variety of fields. |
Contents
Introduction | 1 |
Lagrangian DAES of Motion | 3 |
67 | 36 |
24 | 72 |
Hamiltonian DAEs of Motion | 85 |
Variable Pairs | 99 |
Modeling and Simulation | 115 |
Afterword | 143 |
150 | |
151 | |
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Common terms and phrases
algebraic analytical dynamics applied efforts capacitor co-content coefficients components configuration coordinates constitutive laws constraint efforts DAE in descriptor descriptor form differential equations displacement constraints dynamic constraints effort constraints electrical electromagnetic suspension energy and coenergy energy functions equations of motion example expressed FIGURE first-order ODEs flow constraints fluid Hamilton's equation Hamiltonian DAES Hamiltonian formulation holonomic systems ideal dissipator implicit efforts inductor integral Jacobian kinetic efforts kinetic energy kinetic flows kinetic stores Lagrange Lagrange multipliers Lagrange's equation Lagrange's principle Lagrangian and Hamiltonian Lagrangian DAE Legendre transform linear method momenta momentum multidisciplinary systems multipliers nonholonomic nonholonomic systems nonlinear nonpotential efforts numerical parameters physical systems potential efforts potential energy potential stores reduced-order coordinates represent representational variables resistor semiexplicit form shown in Fig solution solver solving Substituting system dynamics system is given trajectory transducers underlying ODE vector velocity virtual displacements voltage yields ба эт