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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.

1 12 3 0, 1, 2,,, , , n ji i jt i ji n adq adt j m aqqqqtψ = +== = ∑ l l • Constraints of this type are non-integrable and restrict the velocities of the system. 1 0, 1, 2, n ji i jt i aq a j m = ∑ D += =l How determine if a differential equation is integrable and therefore holonomic? • Integrable equations must be exact, i.e. they ...

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