Imagine a pendulum with \(n\) segments. The \(i^{th}\) joint will connect the \((i-1)^{th}\) segment to the \(i^{th}\) segment. Let \(\mathbf{\theta} \in \mathbb{R}^n\) denote the \(n\) internally defined joint angles, \(\mathbf{r} \in \mathbb{R}^{n+1}\) the locations of the \(n\) joints with respect to the global origin, \(\mathbf{\omega} \in \mathbb{R}^n\) the segment rotational velocities, and \(\mathbf{\alpha} \in \mathbb{R}^n\) the segment rotational accelerations. It follows that
\(r_{i} = r_{i-1} + l_i*(sin(\theta_{i})\hat{i}-cos(\theta_{i})\hat{j})\)
\(omega_{i} = \dot{\theta}_i\hat{k}\)
\(alpha_{i} = \ddot{\theta}_i\hat{k}\)
Yet to come: Latex describing equation of motion generation
