Mathematical Pendulum DGL

Question

I've been given the problem regarding a mathematical pendulum: $$\ddot{\phi}=-g\cdot sin\phi -c\cdot \dot {\phi} $$ where $-c\cdot \dot {\phi} $ is the friction within the joint and l=1m, m=1kg.
I've been asked to convert it into a system of first order differential equations by adding a variable and then examine the points of stability.

I'm pretty sure that the stability part i can do, but I'm having trouble finding a place to start with the conversion to a system. We've delt with $$\ddot{\phi}=\frac {-g}{l}\cdot sin\phi $$ in class, which we solved by setting $$\phi ' = \frac {1}{l}v $$ $$v(t)=l\cdot \phi '(t) $$ $$v'(t)=-g\cdot sin \phi $$ and I understand the similarities but the difference is really throwing me off.

How do I approach this problem in order to solve it?

Edit: think I may have copied something wrong in class (or not understood). This form is clearer to me: \begin{align} \dot{\phi}&=\frac{1}{l}v \\ \dot{v}&=-g\cdot sin\phi \\ \ddot{\phi}&=\frac{1}{l}\dot{v} \\ &=-\frac{g}{l}sin\phi\\ \end{align}

Answer 1

Since you have \begin{align} \ddot \phi = -g\sin\phi -c \dot\phi \end{align} then by setting $v = \dot \phi$ we get the system \begin{align} \dot \phi=&\ v\\ \dot v =&\ -g \sin \phi -cv. \end{align} or in matrix form \begin{align} \begin{bmatrix} \dot \phi\\ \dot v \end{bmatrix} = \begin{bmatrix} 0 & 1\\ 0 & -c \end{bmatrix} \begin{bmatrix} \phi\\ v \end{bmatrix} + \begin{bmatrix} 0\\ -g\sin \phi \end{bmatrix}. \end{align}