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profoundphysics.com
Lagrangian Mechanics For Dummies: An Intuitive Introduction – Profound Physics
Often the most common approach to describing motion and dynamics is through Newton's laws, however, there is a much more fundamental approach called Lagrangian mechanics.…
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A two-dimensional orthogonal system is described by the coordinates q1 and q2. Show that the JacobianJ((x, y)/(q1, q2)) = (∂(x, y))/(∂(q1, q2)) = (∂ x)/(∂ q1)(∂ y)/(∂ q2) - (∂ x)/(∂ q2)(∂ y)/(∂ q1) = h1 h2is in agreement with Eq. (2.10).Hint. It's easier to work with the square of each side of this equation.dqJ = dsi dsj = hi hj dqi dqj(2.10)
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