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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 .. whatever this great man says, deserves the highest degree of consideration, but he is too abstract for youth -- student at Ecole Polytechnique.

Lagrange’s Equation • For conservative systems 0 ii dL L dt q q ∂∂ −= ∂∂ • Results in the differential equations that describe the equations of motion of the system Key point: • Newton approach requires that you find accelerations in all 3 directions, equate F=ma, solve for the constraint forces,

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