Find the force function for a particle subject to a central

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SUMMARY

The discussion focuses on deriving the force function for a particle in a central field, specifically for the orbits defined by the equations r = r₀ cos(θ) and r = r₀ e^(kθ). Participants emphasize the need to work in polar coordinates and consider both radial and azimuthal components of acceleration. The relationship between force and angular momentum in a central field is also highlighted as crucial for solving the problem. The consensus is that taking the derivative of the orbit is necessary, but it must be approached correctly to yield accurate results.

PREREQUISITES
  • Understanding of polar coordinates in physics
  • Knowledge of central force fields
  • Familiarity with derivatives and their applications in motion
  • Concept of angular momentum in classical mechanics
NEXT STEPS
  • Study the derivation of force functions in central force problems
  • Learn about the relationship between angular momentum and central forces
  • Explore the use of polar coordinates in dynamics
  • Investigate the mathematical properties of the functions r = r₀ cos(θ) and r = r₀ e^(kθ)
USEFUL FOR

Students of classical mechanics, physicists working on orbital dynamics, and anyone interested in the mathematical modeling of forces in central fields.

Futurestar33
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Homework Statement



The problem is stated as Find the force function for a particle subject to a central field for each of the orbits as follows
a.) r=roCosθ
b.) r=roe^kθ[/B]

Homework Equations


We know the F(x)= dv/dx

here I am assuming F(x)=dv/dθ

The Attempt at a Solution



Do I just take the derivative of the orbit. I believe so but it must be in a different way.
Should I make r=√(x^2+y^2) or simply just take the derivative?
 
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I don't think that either F(x)=dv/dx or dv/d theta. You could have mdv/dt or mv dv/dx.
 
Futurestar33 said:

Homework Statement



The problem is stated as Find the force function for a particle subject to a central field for each of the orbits as follows
a.) r=roCosθ
b.) r=roe^kθ[/B]Do I just take the derivative of the orbit. I believe so but it must be in a different way.
Should I make r=√(x^2+y^2) or simply just take the derivative?

Work in polar coordinates. What are the radial and azimuthal components of the acceleration? What do you know about the angular momentum in a central field?
 

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