Find the force function for a particle subject to a central

AI Thread Summary
To find the force function for a particle in a central field, the discussion emphasizes the need to work in polar coordinates and consider the specific orbits given. Participants suggest taking derivatives of the orbit equations, r=roCosθ and r=roe^kθ, to derive the force function. There is uncertainty about whether to use F(x)=dv/dx or F(x)=dv/dθ, indicating a need for clarity on the relationship between force and motion in polar coordinates. The conversation also touches on the importance of understanding radial and azimuthal components of acceleration and the role of angular momentum in central fields. Overall, the focus is on correctly applying calculus and physics principles to derive the desired force function.
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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