Example: Find the radial and transverse acceleration of a particle moving in a plane curve in Polar coordinates.
How can we use this example to solve our original catenary problem?
We know [math] \tan{\psi}=\frac{s}{a}, s=c\cdot \sinh{\frac{X}{c}}, V_0 = c , e^\psi= \cosh{\psi} + \sinh{{\psi}}[/math]
I am able to get the magnitude of velocity [math]V = c\cdot e^{\psi=0}=c,V = V_0\cdot e^{\psi}[/math] but i am not getting magnitude of acceleration [math]\|\vec{a}\|= \frac{\sqrt{2}}{c} \cdot c^2 \cdot e^{2\psi} \cdot \cos^2{\psi}[/math]