Taking the total differential of "'r "'obtains the transformation of velocity "'v "'to the generalized coordinates, generalized velocities, and coordinate time
12.
In order for the above form to be nonholonomic, it is also required that the left hand side neither be a total differential nor be able to be converted into one, perhaps via an integrating factor.
13.
An " exact differential " is sometimes also called a'total differential', or a'full differential', or, in the study of differential geometry, it is termed an exact form.
14.
In mathematics, an "'exact differential equation "'or "'total differential equation "'is a certain kind of ordinary differential equation which is widely used in physics and engineering.
15.
It is also possible to calculate the total differential of the Hamiltonian \ mathcal { H } with respect to time directly, similar to what was carried on with the Lagrangian \ mathcal { L } above, yielding:
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Which has a similar form to the total differential of " L ", but the virtual displacements and their time derivatives replace differentials, and there is no time increment in accordance with the definition of the virtual displacements.
17.
Albert Einstein ( 1931 ) : " Before Maxwell people conceived of physical reality in so far as it is supposed to represent events in nature as material points, whose changes consist exclusively of motions, which are subject to total differential equations.
18.
Equivalently, any coordinates on phase space which preserve this structure for the canonical one-form, up to a total differential ( exact form ), may be called canonical coordinates; transformations between different canonical coordinate systems are known as canonical transformations.
19.
For this, they should use the total differential, so the current formula lacks a term, correct ? ( Maybe that discussion should be kept at Talk : Stackelberg competition # term missing . ) Common Man 01 : 43, 24 October 2005 ( UTC)
20.
The first and second law have been formulated in terms of time derivatives of " U " and " S " rather than in terms of total differentials d " U " and d " S " where it is tacitly assumed that d " t " > 0.
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