Computation in classical mechanics
نویسندگان
چکیده
منابع مشابه
Irreversibility in Classical Mechanics
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to describe of the nonpotential interaction of a systems. The procedure of splitting of a system into equilibrium subsystems, presentation of subsystem’s energy ...
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here xi = (xi1, . . . , xid) are coordinates of the i-th particle and ∂xi is the gradient (∂xi1 , . . . , ∂xid); d is the space dimension (i.e. d = 3, usually). The potential energy function will be supposed “smooth”, i.e. analytic except, possibly, when two positions coincide. The latter exception is necessary to include the important cases of gravitational attraction or, when dealing with ele...
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supportive in the design process. For this to be possible, computation must be understood in a broad sense, encompassing both the narrow, digital kind of computation and the more general kind of computation in which objects may only have digital approximations. It is this broad approach that we have adopted. The aspects of computation considered here are representation and process. Representati...
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(1) irii'ii = -gradiU(ql9 ..., qn), i = 1, ..., n, where gradf denotes the gradient with respect to q(. Thoughout this paper we use a single dot over a variable to represent its derivative with respect to time t and a double dot to represent its second derivative with respect to t. The potential energy U has a singularity whenever q(=q^ We write this singular set ^v = {€€(«?: *, = *,}, A = U Au...
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I usually do not go to conferences which have in the title the standard fashionable words ”Quantum Gravity” (QG). I made an exception this time because my dear friend Giampiero had the good taste of creating two sessions: one dedicated to QG and another to ”Foundations of Quantization”(FQ). In fact I belong to that minority which thinks that we should not only try to attack the second of the tw...
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ژورنال
عنوان ژورنال: American Journal of Physics
سال: 2008
ISSN: 0002-9505,1943-2909
DOI: 10.1119/1.2870575