Second order differential equation Lagrange mechanics

[player1_1_1]

Homework Statement

from one thing in Lagrange mechanics (general coordinates: $$\phi,\dot\phi,s,\dot{s}$$) I got a equation system:
$$\begin{cases}R\ddot\phi\sin\phi+R\dot\phi^2\cos\phi+\ddot{s}=0\\ g\sin\phi+R\ddot\phi+\ddot{s}\sin\phi=0\end{cases}$$

The Attempt at a Solution

Is it good idea to make a thing which is approximating a equations for little $$\phi$$ and do it like this $$\sin\phi\approx\phi,\quad\cos\phi\approx1$$?

 

[mighty2000]

Hello there, great question! It is definitely a good idea to approximate equations in order to simplify them and make them more manageable. However, it is important to keep in mind the limitations of these approximations. In this case, using \sin\phi\approx\phi,\quad\cos\phi\approx1 may work for small values of \phi, but may not be accurate for larger values. It may be worth exploring other approximations or methods to solve this system of equations. Additionally, make sure to double check your final solution using these approximations to ensure its validity. Good luck with your research!