Automatic generation and integration of equations of motion by operator over-loading techniques
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This paper presents a new method for the automatic generation and integration of equations of motion using operator overloading techniques. An automatic differentiation tool (OCEA: Object Oriented Coordinate Embedding Method) is utilized to compute the partial derivatives required for implementing the traditional Lagrangian equations of motion. The user only builds the kinetic and potential energy. OCEA also builds the equation of motion sensitivity models. Unlike symbolic approaches, the OCEA-Lagrangian method builds the model on-the-fly, no complex pre-processing program must be developed for implementing Lagrange's method. The new method combines the best of the symbolic and numerical equation of motion generation methods, while retaining the simplicity and elegance of the original Lagrangian method. Several examples are presented to illustrate the method.