Well the following content on curvilinear kinemetics will help.

 

 

 

 

Curvilinear Kinematics investigates lows of motion of objects in space in two and three directions without any reference to forces that cause the motion to change

Here

 is original time on time interval

 is final time

 is position vector at time

 is position vector at time

 is displacement vector during time

 is length of path during time

  is mean velocity vector during time

 is instantaneous velocity vector at time , tangent to trajectory

is total acceleration vector at time

are unit vectors of axes x, y, z respectively

 

 

 

Where:

R is radius of curvature of trajectory at time

is centripetal acceleration, normal to trajectory and directed to its center

is tangential acceleration, tangent to trajectory and parallel to velocity

is total acceleration vector