# Lagrange's Equation with Multiple Degrees of Freedom

1. Sep 24, 2015

### mwspice

Hi,

I'm currently trying to learn about finding equations of motion from the Lagrange equation, and I'm a little confused about how it applies to multiple degree of freedom systems. I am using the following form of the equation with T as total kinetic energy, V as total potential energy, R as Rayleigh's dissipative function, $q_i$ as the generalized coordinate, and $Q_i$ as a generalized non-conservative force. For a MDOF system, do I have to do this equation once for each DOF?

$\frac{d}{dt} \left( \frac{\partial T}{\partial \dot q_{i}} \right) - \frac{\partial T}{\partial q_{i}} + \frac{\partial V}{\partial q_{i}} + \frac{\partial R}{\partial \dot q_{i}} = Q_i$

Thanks

Last edited: Sep 24, 2015
2. Sep 24, 2015

### MisterX

Yes, you will have a differential equation for each value of $i$ creating a system of differential equations.

3. Sep 24, 2015

### mwspice

Thank you for your reply! So what is the best way to solve the resulting system of equations? Is it best to just try to use a software like MATLAB to find numerical solutions, or is there a good method for decoupling and solving the equations? If you could point me towards any good resources for this topic, that would also be very much appreciated.

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