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Lecture #7 Lagrange's Equations - MIT OpenCourseWare

Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology How, Deyst 2003 (Based on notes by Blair 2002) 1 Lecture #7 Lagrange's Equations Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology How, Deyst 2003 (Based on notes by Blair 2002) 1 Lagrange s Equations Joseph-Louis Lagrange 1736-1813 ~history/ Born in Italy, later lived in Berlin and Paris. Originally studied to be a lawyer Interest in math from reading Halley s 1693 work on algebra in optics If I had been rich, I probably would not have devoted myself to mathematics. Contemporary of Euler, Bernoulli, Leibniz, D Alembert, laplace , Legendre (Newton 1643-1727) Contributions o Calculus of variations o Calculus of probabilities o Propagation of sound o Vibrating strings o Integration of differential Equations o Orbits o Number theory o.

Laplace, Legendre (Newton 1643-1727) • Contributions o Calculus of variations ... Example: Work in polar coordinates, then transform to rectangular coordinates, e.g. sin cos ... Existence of constraints complicates the solution of the problem.

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