Galileo made essential contributions to the development of inertial mechanics. His two most basic contributions were to collect the set of problems that held the keys to inertial mechanics and then address them all with an effective, consistent mechanics.
Classical mechanics is still taught by referring new students to the core set of problems that had to be solved by the original investigators like Descartes, Gassendi, Huygens, Wallis, Wren, Hooke, and Newton, all following Galileo's original line of attack. These problems include the analysis of motion on an inclined plane, the motion of a pendulum, the action of a lever, the force of a spring or pull in a rope, the result of collisions between impacting and moving bodies, and so on.
Inertial mechanics was extended to a far wider range of problems, but no writer before Galileo had put so many of the basic problems together in a single, articulate discussion. For that reason alone we may describe Galileo's work as modern in character and properly within the bounds and spirit of classical mechanics, even though the elements of the latter system were not successfully elaborated for almost fifty years after his passing and in spite of the fact that he sometimes proposed mistaken ideas to solve the basic problems.
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