I really appreciate the recommendations. I have enough knowledge of the field to understand that control engineering and vibrational modes are extremely important but not enough to know what's most important to know about them or which books are more reliable or better written.

I don't have experience with your kinematics book, and have some limited exposure to machinery's handbook. My impression of the latter is that it is good and highly regarded, but perhaps more on the Practical fabrication side then engineering Theory.