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The action principles have applications as broad as physics, including many problems in classical mechanics but especially in modern problems of quantum mechanics and general relativity. These applications built up over two centuries as the power of the method and its further mathematical development rose.
The physical content of these different formulations is the same, but they provide different insights and facilitate different types of calculations. While the term "Newtonian mechanics" is sometimes used as a synonym for non-relativistic classical physics, it can also refer to a particular formalism based on Newton's laws of motion.
"High school physics textbooks" (PDF). Reports on high school physics. American Institute of Physics; Zitzewitz, Paul W. (2005). Physics: principles and problems. New York: Glencoe/McGraw-Hill. ISBN 978-0078458132
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
Physics – branch of science that studies matter [9] and its motion through space and time, along with related concepts such as energy and force. [10] Physics is one of the "fundamental sciences" because the other natural sciences (like biology, geology etc.) deal with systems that seem to obey the laws of physics. According to physics, the ...
With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle. With respect to symmetries and invariance principles, three special conservation laws have been described, associated with inversion or reversal of space, time, and charge.
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles.