Change in the direction of motion of the particle

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SUMMARY

The discussion centers on the change in the direction of motion of a particle transitioning between two half-spaces with different potential energies, U1 and U2. Participants reference the Hamilton variational principle and draw parallels to the refraction of light as a potential analogy for solving the problem. The challenge lies in applying these concepts to determine the particle's new trajectory upon entering the second half-space. No definitive solutions were provided, indicating a need for deeper exploration of Analytical Mechanics principles.

PREREQUISITES
  • Understanding of Analytical Mechanics
  • Familiarity with the Hamilton variational principle
  • Knowledge of potential energy concepts
  • Basic principles of particle motion and trajectory analysis
NEXT STEPS
  • Study the application of the Hamilton variational principle in particle dynamics
  • Research the principles of refraction in physics
  • Explore potential energy transitions and their effects on particle motion
  • Learn about trajectory analysis in Analytical Mechanics
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Students of physics, particularly those studying Analytical Mechanics, as well as educators and anyone interested in the application of variational principles to particle motion problems.

TheDispStud
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Homework Statement
A particle of mass m moving with velocity v1, leaves a half-space in which the potential is a constant U1 and enters the other half-space, where the potential energy is a different constant U2.
Relevant Equations
Determine the change in the direction of motion of the particle.
Unfortunately, I have no idea about a possible solution.
 
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TheDispStud said:
Homework Statement:: A particle of mass m moving with velocity v1, leaves a half-space in which the potential is a constant U1 and enters the other half-space, where the potential energy is a different constant U2.
Relevant Equations:: Determine the change in the direction of motion of the particle.

Unfortunately, I have no idea about a possible solution.
In which context did this question come up? Have you studied the variational principle?
 
Yes, we discussed about the Hamilton variational principle.
 
TheDispStud said:
Yes, we discussed about the Hamilton variational principle.
Does this question look similar to the refraction of light?
 
This is an exercise of Analytical Mechanics :-)
 
TheDispStud said:
This is an exercise of Analytical Mechanics :-)
What would Hamilton say in this case?
 
I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!
 
TheDispStud said:
I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!
I've given you two ideas: refraction and Hamilton's principle. It's up to you to show us something based on those ideas.
 

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