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Variational principles are found among earlier ideas in surveying and optics.The rope stretchers of ancient Egypt stretched corded ropes between two points to measure the path which minimized the distance of separation, and Claudius Ptolemy, in his Geographia (Bk 1, Ch 2), emphasized that one must correct for "deviations from a straight course"; in ancient Greece Euclid states in his ...
Lorentz factor: unitless photon: gamma ray: shear strain: radian heat capacity ratio: unitless surface tension: newton per meter (N/m) delta: change in a variable (e.g. ) unitless Laplace operator: per square meter (m −2) displacement (usually small) meter (m) Dirac delta function
C.G. Gray, G. Karl, and V. A. Novikov, "Progress in Classical and Quantum Variational Principles". 11 December 2003. physics/0312071 Classical Physics. Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. John Venables, "The Variational Principle and some applications". Dept of Physics and ...
The conceptual differences between physics theories discussed in the 19th century and those that were most historically prominent in the first decades of the 20th century lead to a characterization of the earlier sciences as "classical physics" while the work based on quantum and relativity theories became known as "modern physics".
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1]
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.
The early identification of self-similar solutions of the second kind can be found in problems of imploding shock waves (Guderley–Landau–Stanyukovich problem), analyzed by G. Guderley (1942) and Lev Landau and K. P. Stanyukovich (1944), [3] and propagation of shock waves by a short impulse, analysed by Carl Friedrich von Weizsäcker [4] and ...
Perturbation theory has been used in a large number of different settings in physics and applied mathematics. Examples of the "collection of equations" include algebraic equations, [6] differential equations [7] (e.g., the equations of motion [8] and commonly wave equations), thermodynamic free energy in statistical mechanics, radiative ...