I just had a classical mechanics exam where there is a question asking about a movement of mass m moving in a parabola, where Z=(1/2)a(x^2+y^2). gravity acts as -mg^z
The first parts asks to express the motion in cylindrical coordinates and find its virtual displacement. The second part asks to find second derivative with generalized coordinates Then by calculating virtual work done by inertia and by applied force and thus calculate the equation of motion with d'Alembert principle.
so for part 1 I wrote r(^r)=s(s^)+ z(^z) =s(^s)+(1/2)a(s^2)(^z), and then calculated the virtual displacement. For second part, I just copied the second derivative of r(^r) from formula sheet (I did not forget to put in z=(1/2)a(s^2)(^z)) However, as I proceed, I got some funny answers and did not reach to something that looks meaningful.
Can anyone help me write the virtual displacement and second derivative of r(^r) down? Sorry if this looks really messy, I am new to this forum