What Is the Kinetic Energy Equation for a Mass on a Double Pendulum?

[Axecutioner]

You can treat the cable as another rigid bar in this case, both massless. I just need the equation for the Kinetic Energy of the mass on the end.

Is there an equation for if the main bar is torqued at a given τ(t), and any other necessary information is given, to find the position of the mass on the end or the angles of the two bars at any given time?

I'm in a Statics class right now and will be taking advanced dynamics in the fall but I'd like to work on a personal project in the fall. Done through Calc 4 and Stokes Theorem if it matters.

Thanks

 

[thebrainstorm]

Burn the thread. The ball will remain and will perform free fall. Then you will easily get your answer.

 

[Axecutioner]

That doesn't help at all.

I know K = 1/2*I*w^2 but what would the omega be? Just both angular velocities added together?

 

[Axecutioner]

Sorry, misunderstanding. Please delete this post.

 

[asteriatic]

for your question. The double pendulum is a classic problem in mechanics that can be solved using a variety of mathematical techniques, including calculus and Stokes' theorem. The equation for the kinetic energy of the mass on the end of the double pendulum will depend on the positions and velocities of both masses, as well as the length and mass of the bars.

To find the position of the mass on the end or the angles of the two bars at any given time, you will need to use the equations of motion for the double pendulum, which can be derived using Lagrangian mechanics. These equations will involve the angles and angular velocities of the two bars, as well as the torques acting on the system.

I would recommend studying the dynamics of the double pendulum in more depth, as it is a complex and fascinating problem with many potential solutions. I also encourage you to continue exploring the use of advanced mathematical techniques, such as Stokes' theorem, in solving physical problems. Good luck with your personal project!