- #1

fog37

- 1,568

- 108

For 2D motion, I understand that velocity, position and acceleration of a point object can be described using the fixed basis vector ##\hat {i}## and ##\hat {j}## and the rectangular coordinates ##x(t)## and ##y(t)## which which are functions of time ##t##.

Another option is to use the tangential (to the trajectory) unit vector ##\hat {e}_t## and the normal (to the trajectory) unit vector ##\hat {e}_n##. Are the components of the tangential and normal unit vectors supposed to be functions of time ##t## or functions of the scalar arc-length ##s##?

Also, why are the tangential and normal unit basis vectors called intrinsic? When is the motion description with these two basis vectors more useful than a description involving the traditional rectangular coordinates?

Thanks!