Quick Question in projectile motion (H-J)

Thread starter M. next
Start date Jul 2, 2012
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Motion Projectile Projectile motion

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In the context of the Hamilton Jacobi Equation for projectile motion in two dimensions, the classification of x as a cyclical coordinate is contingent on the specific Hamiltonian being analyzed. A cyclical coordinate implies that the coordinate does not explicitly appear in the Hamiltonian, allowing for conservation of momentum in that direction. The discussion emphasizes the importance of examining the Hamiltonian to determine the nature of the coordinates. The determination of whether a coordinate is cyclical or non-cyclical can significantly impact the analysis of the system. Ultimately, the classification of x as cyclical is not universally applicable and depends on the details of the Hamiltonian.

Jul 2, 2012

M. next

In Hamilton Jacobi Equation (Projectile in two dimentions [x,y]), Isn't it correct that x is a cyclical coordinate?

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Jul 3, 2012

Simon Bridge

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You could figure that out by considering what "cyclical coordinate" means, then examining your Hamiltonian with this in mind. Of course, you can anticipate the answer from the way that a coordinate becomes non-cyclical.

The quick answer is: depends.

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