Quick Question in projectile motion (H-J)

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SUMMARY

The discussion centers on the classification of the x-coordinate as a cyclical coordinate in the context of the Hamilton-Jacobi Equation for projectile motion in two dimensions. Participants emphasize the importance of understanding the definition of cyclical coordinates and analyzing the Hamiltonian to determine the nature of the coordinates. The conclusion drawn is that the classification of x as cyclical or non-cyclical depends on specific conditions outlined in the Hamiltonian analysis.

PREREQUISITES
  • Understanding of Hamilton-Jacobi Equation
  • Knowledge of cyclical coordinates in classical mechanics
  • Familiarity with Hamiltonian mechanics
  • Basic concepts of projectile motion in two dimensions
NEXT STEPS
  • Study the properties of cyclical coordinates in Hamiltonian systems
  • Examine the derivation and implications of the Hamilton-Jacobi Equation
  • Explore examples of projectile motion using Hamiltonian mechanics
  • Learn about non-cyclical coordinates and their impact on motion analysis
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Students and professionals in physics, particularly those studying classical mechanics, Hamiltonian dynamics, and projectile motion analysis.

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