A Lagrangian Multipliers with messy Solution

[Mishal0488]

Hi Guys

Please refer to the attached file.
I have not included any of the derivatives or partial derivatives as it does get messy, I just just included the kinetic and potential energy equations and the holonomic constraint.

The holonomic constraint can be considered using Lagrange multipliers. The result is 4 equations, one for each coordinate and the holonomic constraint.

I am not sure what to do once I am at this point, can someone please assist?
With regards to the holonomic constraint, I can make one of the variables the subject of the formula, however due to the squared terms there are two equations which will arise.

Kind regards
Mishal Mohanlal

 

[hagopbul]

look like a known problem in solid state physics but i am not able to remember it now did you try matrix method for differential equations

 

[Mishal0488]

Why solid state physics? The image is a mechanical system which I am trying to simulate.

Note that I am an engineer and my understanding of Lagrangian mechanics is limited since it is not taught as part of engineering. I have learned through self study.

I was hoping to develop the system of equations and thereafter solve it using Runge Kutta