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Fill in the details of the derivation of Hamilton's 2n

Chapter 13, Problem 13.15

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QUESTION:

Fill in the details of the derivation of Hamilton's 2n equations (13.25) for a system with n degrees of freedom, starting from Equation (13.24). You can parallel the argument that led from (13.14) to (13.15) and (13.16), but you have 2n different derivatives to consider and lots of summations from i = 1 to n to contend with.

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QUESTION:

Fill in the details of the derivation of Hamilton's 2n equations (13.25) for a system with n degrees of freedom, starting from Equation (13.24). You can parallel the argument that led from (13.14) to (13.15) and (13.16), but you have 2n different derivatives to consider and lots of summations from i = 1 to n to contend with.

ANSWER:

Step 1 of 3

According to Eq. (13.24)

                                        (S13.6)

 

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