I previous had some exposure to rigid body dynamics using the more conventional Lie group notation used in robotics (as seen here: http://hades.mech.northwestern.edu/index.php/Modern_Robotics and https://www.cs.cmu.edu/~junggon/tools/liegroupdynamics.pdf). But I felt the Lie group theory surrounding it were hard to understand (I don't have that much exposure to abstract algebra, I wasn't a mathematics major).

So you think would PGA aid in understanding the weird properties of SO(3) and SE(3) (and its tangent spaces), as well as writing simulation code with it? I know that people use various representations for rigid transformations (screws vs. dual quaternions vs. exponential maps vs. motors), but I am interested which method would work the best in both a theoretical sense (in understanding the kinematics and dynamics more abstractly) and in a pragmatic sense (difficulty of writing and reading actual simulation code, amount of operations used, SIMD-friendliness, etc.)