Hamilton's Principle Equations! Work Shown Please Help! A particle of mass m moves under the influence of gravity alng the helix z=k(theta), and r=R, where R and k are constants and z is vertical. a.) Using cartesian co-ordinates, write down the expressions for the kinetic energy of the system. b.) Change to cylindrical co-ordinate system using x= rcos(theta) y= rsin(theta) express your eq for the kinetic energy as a function of the new co-ordinates. Give also expressions for the potential energy and the Langrangian of the system (in cylindrical co-ordinates). c.) How many degrees of freedom do you have for this system? Name them (or it) d.) Calculate the equation(s) of motion using the Langrange equation for this system. my work: a.) T= 1/2 m(x*time-deriv.)^2 + 1/2(y*time-deriv)^2 + 1/2(k(theta)*time-deriv.)^2 b.) if x= rcos(theta) and y=rsin(theta) equation for kinetic energy in terms of cylin. co-ord is: x= rcos(theta) y= rsin(theta) therefore, x-time deriv.= r*angle-timederiv. cos(theta) y-time deriv.= r*angle-timederiv.sin(theta) therefore, kinetic energy in cylin. co-ord. T= (1/2)*(m)[(r*time-deriv)+(r^2*angletimederiv^2)+(ztimederiv^2)] and therefore potential energy equals: U=mgz therefore the langrangian of the system in cylin. co-ord equals: since z=k(theta) and r=R therefore langrangian equals (L)= (1/2)*(m)[(R^2/k^2)(ztimederiv^2)+(ztimederiv^2)] -mgz c.) need some help here, i believe the degree of freedom is six: since in three dimensions, the six DOFs of a rigid body are sometimes described using these nautical names: Moving up and down (heaving); Moving left and right (swaying); Moving forward and backward (surging); Tilting forward and backward (pitching); Turning left and right (yawing); Tilting side to side (rolling). not sure if this is correct need help d.) using langrangian equation: z-2ndtime deriv= g/[(r^2/k^2)+1] need help proving that PLEASE HELP A LOT OF WORK SHOWN NEED HELP HERE!