# How to find angular velocity using pure pursuit algorithm?

I have implemented the pure pursuit algorithm for my differential wheeled robot as described in the following paper:

http://www.enseignement.polytechnique.fr/profs/informatique/Eric.Goubault/MRIS/coulter_r_craig_1992_1.pdf

Such that the steering angle is given by λ=2x/l^2

I want the robot to have a constant linear velocity V (say of 0.5m/s) but I am unsure of how I'd go about finding the angular velocity ω using this calculated steering angle.

I wish to plug the angular and linear velocity into the following inverse kinematics formuala for a differential wheeled robot as shown in the figure below.

Where the formulas are described in section 3.2.2 'Introduction to Autonomous Mobile Robots' found here:

https://ieeexplore.ieee.org/book/6267528

I'm unsure of what I need to do to translate the steering angle into a form where it can be input into the formula described above for each of the wheel speeds. I'm sure there is a simple solution but I am lost as to the next steps to take