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Summary:
 What can I expect to get if I take the derivative of velocity with respect to position? Is it zero?
I'm reading a book on Classical Mechanics (No Nonsense Classical Mechanics) and one particular section has me a bit puzzled. The author is using the EulerLagrange equation to calculate the equation of motion for a system which has the Lagrangian shown in figure 1. The process can be seen in figure 2. What I don't understand is this:
He seems to consider that the partial derivative of (dx/dt)^{2} with respect to x is zero. Same thing for the partial derivative of x^{2} with respect to dx/dt. This doesn't seem obvious to me and I haven't found any explanations elsewhere. Why is it so?
He seems to consider that the partial derivative of (dx/dt)^{2} with respect to x is zero. Same thing for the partial derivative of x^{2} with respect to dx/dt. This doesn't seem obvious to me and I haven't found any explanations elsewhere. Why is it so?
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