How can I integrate an acceleration vector in polar coordinates?

[AirForceOne]

Hi,

Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j.

How can I integrate that vector so that I have the velocity vector in polar coordinates?

I know that if I have an acceleration vector in Cartesian coordinates: a = -30j, I can integrate it with respect to time to get v = (-30t+v_0y)j + (v_0x)i.

I feel like integrating an acceleration vector in Cartesian coordinates is easier because i and j do not change as the tip of the vector moves around over time. However, with polar coordinates, e_r changes direction and yeah it gets messy.

Thanks.

 

[fresh_42]

Simply integrate it by the easier coordinates. That's why integration in polar coordinates are considered! If Cartesian is easier, then use it and transform the result afterwards in case you need polar coordinates.