Y.V. Venkatesh's Energy Methods in Time-Varying System Stability and PDF

By Y.V. Venkatesh

ISBN-10: 3540084304

ISBN-13: 9783540084303

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Additional info for Energy Methods in Time-Varying System Stability and Instability Analyses

Sample text

MOLECULAR ROTATION. 15 There is, as was first shown by Sir G. Stokes, an important 20. physical distinction in the character of the motion which takes place, according as a velocity potential does or does not exist. Conceive an indefinitely small spherical element of a fluid motion to become suddenly solidified, and the fluid about it to be suddenly destroyed. By the instantaneous solidification, in be suddenly generated or destroyed in the different and a set of mutual impulsive forces will velocities will portions of the element, be called into action.

1 1 I EXAMPLES AND APPLICATIONS. 25 A 33. radius mass of liquid whose external surface is a sphere of and which is subject to a constant pressure II, surrounds The solid sphere is annihilated, it is sphere of radius b. a, a solid required It is place, is to determine the motion of the liquid. evident that the only possible motion which can take one in which each element of liquid moves towards the R whence the free surfaces will remain spherical. Let R\ be their external and internal radii at any subsequent time, r the distance of any point of the liquid from the centre.

We shall however find it simpler in the case of a sphere, to which we shall proceed to solve the do. problem directly, Let the sphere be moving along a straight line with velocity V, and let (r, 6, - The boundary condition, which expresses the fact, that the normal component of the velocity of the liquid at the surface of the sphere, is equal to the normal component of the velocity of the sphere itself, is ^ = Fcos0 (33).

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Energy Methods in Time-Varying System Stability and Instability Analyses by Y.V. Venkatesh

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