My favorite physics problem not is not an end-of-chapter problem

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In physics pedagogy, the common approach involves introducing new concepts during lectures followed by practicing through end-of-chapter problems. A specific problem, referred to as the Kepler problem, is highlighted as a favorite among participants, emphasizing its significance in intermediate mechanics courses. Mastering the mathematical steps involved in this problem is noted to provide a satisfying learning experience, underscoring the importance of problem-solving in understanding complex physics concepts. Additionally, there is mention of a handwriting machine learning algorithm, indicating a potential intersection of physics with technology and computational methods in education.
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In physics pedagogy, the routine is to introduce new material in lectures and then practice the material in end-of-chapter problems. This problem, shown below, familiar to many of us on PF, is my favorite. One must get to intermediate mechanics class in undergraduate physics studies to finally see it, and once the mathematical steps are mastered, one may find the knowledge gained most satisfying. At least, that’s my experience:

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I bet you can name the problem.
 
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Kepler problem
 
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Some sort of handwriting machine learning algorithm.
 
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