Solving Lagrangian Mechanics Homework in 2D Movement

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SUMMARY

The discussion focuses on solving a Lagrangian mechanics problem involving a particle moving in a two-dimensional plane under a central force. The force is defined as F = -dU/dr, where U represents the potential energy. Participants seek to derive the potential generator expression and the corresponding Lagrangian for this system. Key questions include how to solve the integral involving r and its derivatives, as well as the dependency of dr/dt on the function of r over time.

PREREQUISITES
  • Understanding of Lagrangian mechanics principles
  • Familiarity with central force dynamics
  • Knowledge of calculus, particularly integration techniques
  • Basic concepts of potential energy functions
NEXT STEPS
  • Study the derivation of the Lagrangian for central force problems
  • Learn about solving integrals involving time-dependent variables
  • Explore the relationship between position and velocity in polar coordinates
  • Investigate examples of potential energy functions in Lagrangian mechanics
USEFUL FOR

Students and educators in physics, particularly those studying classical mechanics, as well as anyone interested in applying Lagrangian methods to solve problems in two-dimensional motion.

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Homework Statement


So, a particle is moving in a plane under the action of a force F that is oriented at all times to the direction of the center of the force.may r be the distance from the particle to the center of the force generator.

Find the potential generator expression that occurs and the form of the Lagrangian for 2D movement of the particle.

the force F's expression is below
CodeCogsEqn.gif

.

Homework Equations


Lagrangian mechanics...

The Attempt at a Solution


okay, so F=-dU/dr so
CodeCogsEqn-2.gif
=

CodeCogsEqn-3.gif


And my question is, how do you solve that integral? the one over r 2dot and r dot?? If anyone could explain that to me it would be great!ty
 
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Let me ask you this. If you have r = some function of time, does the function for dr/dt depend on r?
 

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