Homework Solutions On Classical Mechanics
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Classical mechanics is concerned with the study of systems of bodies where the internal forces that act on the bodies are considered to be of a conservative nature. The forces are conservative in the sense that they tend to restore the total mechanical energy of the system to a constant value.
Newton's law of universal gravitation, which describes the gravitational forces between bodies, is one of the first laws of classical mechanics. It was established by Isaac Newton (1642-1727). Newton's third law is the most important law that describes the forces that act between any two bodies. This law states that for every force there is an equal and opposite reaction force. Newton's law of universal gravitation says that bodies attract each other because they are massive and have mass. In addition, the force of gravity decreases inversely as the square of the distance. This law has been verified by experiments to a great degree of precision.
The total energy of a body is the energy that is available for doing mechanical work. It is given by the sum of the kinetic energy and potential energy of the body. The total energy of the system is conserved in the time-evolution of the system. The gradient of the potential energy of the system is a conservative force and acts on each body that is in the system. This force is called the total force on the body. The total force is equal to the force exerted on the body by other bodies in the system due to the mass of the bodies, their location and velocity, as well as the gravitational force.
Recommended texts:  For the course on mechanics, you might want to look at Mechanics by Arnold. The course also uses Arnold's book Mathematical Methods of Classical Mechanics. This book is not required, but you should know the basic ideas in mechanics from it. For a course on special relativity, you might look at the textbook by Landau & Lifshitz, The Classical Theory of Fields. Both of these books are dense and contain lots of important information, but they are better for motivation than for solving problems.
Possible topics:  The first semester will be about momentum and conservation of energy. The second semester will be about conservative forces and forces between electric charges. The third semester will be about springs and strings, and so on. The field of mechanics is vast, and there are many more topics than I can cover.
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