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These quantities are conserved in certain classes of physics processes, but not in all. A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
The physical content of these different formulations is the same as the Newtonian, but they provide different insights and facilitate different types of calculations. For example, Lagrangian mechanics helps make apparent the connection between symmetries and conservation laws, and it is useful when calculating the motion of constrained bodies ...
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
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.
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.
"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
The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. The action principle provides deep insights into physics, and is an important concept in modern theoretical physics. Various action principles and related concepts are summarized below.