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Homework Statement
Homework Equations
L = T-V
The Attempt at a Solution
I got a forumla for the lagrangian as
check the L written above and set up the Lagrange's equations of motion.....I got a forumla for the lagrangian as
Its more I don't know if the L is correct and wanted to check what the derivation is with someone else's because i'm pretty sure my derivation is wrong.check the L written above and set up the Lagrange's equations of motion.....
the lagrangian is T- V , where T is kinetic energy and V is potential energy of the system.Its more I don't know if the L is correct and wanted to check what the derivation is with someone else's because i'm pretty sure my derivation is wrong.
your regulator has two degrees of freedom one described by angle si and the other by angle theta.Its more I don't know if the L is correct and wanted to check what the derivation is with someone else's because i'm pretty sure my derivation is wrong.
You have neglected the rotational inertia of the spheres about their centers. This will add additional terms to T. Also, check the sign of the gravitational potential energy part of L.Its more I don't know if the L is correct and wanted to check what the derivation is with someone else's because i'm pretty sure my derivation is wrong.
Each ball does rotate as either ##\theta## or ##\psi## changes. Consider a ball attached to the end of a stick as shown in the figure below. As the stick rotates through an angle θ, the ball also rotates through θ.I don't believe the balls are allowed to rotate about their centers.
The potential energy is subtracted in the Lagrangian: L = T - V. You got the sign correct for the spring potential energy.Why wouldn't the gravitational potential be positive?
It's just a kinetic energy term due to rotation about the center of mass.Yeah I agree with that, but what other term would that introduce?
If θ increases, both the spring potential energy and the gravitational potential energy increase.Also wouldn't the gravity term be the opposite direction to the spring?
This is not quite the correct expression for ##l##. The ##R/2## part is incorrect. ##l## should be the distance from ##O## to the center of mass of one of the balls.Could you possibly write out the correct Lagrangian as I feel like I'm stumbling around it and would love to inspect the correct one. And sorry there is a note at the start of my work I forgot and it just says
That's getting very close to the correct ##L##. However, you need to include a rotational KE term associated with ##\dot{\theta}## as well as with ##\dot{\psi}##. And, as you say, the coefficient for the gravity terms needs to be corrected.
When evaluating ##\frac{\partial{L}}{\partial \theta}##, how did you get factors of ##\dot{\theta}## to appear?
This expression for ##L## looks correct to me as long as the distance ##l## has the correct interpretation.