Physics textbook covering relative kinematics/dynamics

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PhysicsLad
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My university's professors have a pathological obsession with non inertial frames of reference which apparently has been going on for decades. As a result we work tons of these problems involving kinematics, dynamics and so on.

However, none of the books listed in the bibliography of the course include a chapter on this, and the handouts are as messy as they get (this is the first year this course is taught in English, and the teachers prepared it in a couple of months notice).

So, if I want to pass this course without losing my sanity I really need a book which covers relative kinematics and dynamics rigorously, a rigorous chapter at least. This would be my reference for the whole 8 month + course so it needs to be a decent text overall (if it covers the stuff taught after mechanics like electromagnetism, fluids, thermo... it would make it almost perfect). Everything here is also Calculus heavy.
 
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Do you mean relativistic physics when you say "relative dynamics"? If so then SRT text rarely give a satisfactory treatment of non-inertial frames of reference. An impressive work is

E. Gourgoulhon, Special Relativity in General Frames, Springer 2013

It's of course an overkill for an introductory course ;-).