12.18. In Problem 12.17, if masses m, and m2 simply move in horizontal and vertical straight...

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12.18. In Problem 12.17, if masses m, and m2 simply move in horizontal and vertical straight lines in a uniform gravitational field, set up and solve Lagrange's equations. 12.19. The elliptical coordinates (u, v) of a point mass m are defined by u = A cosh u cos v and y = A sinh u sin v where A is a constant. Calculate the kinetic energy of the particle and its Lagrange's equations. 12.18. In Problem 12.17, if masses m, and m2 simply move in horizontal and vertical straight lines in a uniform gravitational field, set up and solve Lagrange's equations. 12.19. The elliptical coordinates (u, v) of a point mass m are defined by u = A cosh u cos v and y = A sinh u sin v where A is a constant. Calculate the kinetic energy of the particle and its Lagrange's equations.