Analytical system dynamics
A unified approach for modeling engineering systems is presented for systems comprised of mechanical, electrical, fluid and thermal elements. The method of analysis is based on the energy methods of Lagrange, generalized to encompass constrained multidiscipline systems. The physical systems theory is developed within the framework established by Paynter. The result of analysis is a set of differential-algebraic equations (DAE) systematically formulated for numerical solution, thereby providing the engineer with a means of modeling and computation suitable for the analysis of complex engineering systems.A new derivation of Lagrange's equation is given based on a differential-variational form of the first law of thermodynamics. Equations of motion are formulated without posing the problem as a calculus of variations problem and without invoking Hamilton's principle. Undetermined multipliers are used, and a Lagrangian DAE of motion is formulated.By applying a partial Legendre transform to the Lagrangian DAE, a differential-algebraic form of Hamilton's equation is derived. Complementary forms of the Lagrangian DAE and the Hamiltonian DAE are derived. In all cases a nonlinear model is formulated for systematic application to a multidiscipline system. Lagrange's equation and its dual are given as a set of linearly implicit DAEs in descriptor form. Hamilton's equation and its dual are given as a set of semi-explicit DAEs.The formulation of a model as a DAE avoids some of the drawbacks of conventional graphical techniques: a model need not be reduced to a set of independent equations; nonholonomic constraints and system nonlinearities are readily accommodated; and the primary effort of the analyst is directed at obtaining energy functions and equations of constraint rather than drawing a graph to represent the system. A secondary effort is directed at manipulating these functions in a systematic way to obtain the desired set of DAEs. This step is readily automated, and produces a set of equations that are suitable for numerical solution.The procedures of analysis, function manipulation, numerical solution and automation are described. This research, emphasizing analysis and model formulation, lays the foundation for future work in numerical solution and automated modeling of complex engineering systems.
- Mechanical engineering