There is a naive general idea that we already understand classical mechanics very well, but I do not think that is the case. There are many fundamental questions in classical mechanics without a satisfactory answer. One of them is the description of the trajectory of a charged particle in the presence of an electromagnetic field. Yes, we have the Lorentz force, but it does not take into account the effect of the radiation of the charged particle in the acceleration process. The Lorentz-Dirac force is an attempt to include the effect of the radiation but unfortunately, the solutions of this equation are pathological. Most books only mention this situation but Baylis's book in electrodynamics devotes a complete chapter this subject.
Electrodynamics: a modern geometric approach
By William Eric Baylis (chapter 12)
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