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prooflagrange

prooflagrange - derivative Then note that only depends on...

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This equation can be proven by obtaining the first term on the right hand side and then the second term (according to Richardson, 1996). Part 1 The chain rule can be applied first to express the left hand side in terms of expressions containing only the velocity of the position vector: Then the expression in the parenthesis of the first term on the right hand side can be written in terms of the vector product of the velocity vectors: Part 2 The second term in the equation at the top can be proven by expressing the second term in the previous equation in terms of a displacement derivative instead of a velocity

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Unformatted text preview: derivative: Then note that only depends on the generalized displacements so that Next the velocity vector is calculated: and then its partial derivative with respect to the generalized coordinates is calculated: If is twice differentiable, then this equation is the same as the equation for . Therefore, the second expression on the right hand side of this equation can be written as and then the chain rule is applied to the last expression to obtain the equation that we wished to prove:...
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