Equations rotary motion

This makes Vp-Vvp = 0(r ), which obviously gives rise to a particular integral of the perturbation equations of the form v, =0(r ). There is now no difficulty in finding a complementary function to permit satisfying the boundary conditions (192). Whitehead s paradox does not therefore extend to such rotary motions. These may be handled by the conventional perturbation scheme proposed by Whitehead. 

The variational equations of motion are developed for flexible serial manipulators with rotary joints which account for full coupling between the rigid body motion and link deformation. Velocity and acceleration transformation equations are developed to conveniently transform Cartesian space equations into Joint space. Small deformation is assxamed such that vibration modal coordinates and mode shapes can represent the elastic motion of the flexible links. Flexibility and mass properties of the links are obtained by finite element method. A case study of an industrial robot is presented to show the effect of bending and torsional vibrations on end-effector motion. 

The kinetic (rotary diffusion) equation for the particle magnetic moment may be solved with high precision, thus taking into account contributions from the intrawell motions that are essential for a correct description of SR, especially at low temperatures. 

The changes have been used to provide information about the enviromnent of the fluorescent probe and to follow changes in conformation of the macromolecule. In other work the study of the fluorescence polarization properties of the attached probe under steady state illumination and the application of Perrin s equation enable calcu-latnn of the rotary Brownian motion of the polymer. This technique has been extended by Jablonski and Wahl to the use of time-resolved fluorescence polarization measurements to calculate rotational relaxation times of molecules These experiments are discussed fiilly in the fdlowing section of this review. 

For many purposes, it is more convenient to characterize the rotary Brownian movement by another quantity, the relaxation time t. We may imagine the molecules oriented by an external force so that the a axes are all parallel to the x axis (which is fixed in space). If this force is suddenly removed, the Brownian movement leads to their disorientation. The position of any molecule after an interval of time may be characterized by the cosine of the angle between its a axis and the x axis. (The molecule is now considered to be free to turn in any direction in space —its motion is not confined to a single plane, but instead may have components about both the b and c axes.) When the mean value of cosine for the entire system of molecules has fallen to ile(e — 2.718... is the base of natural logarithmus), the elapsed time is defined as the relaxation time r, for motion of the a axis. The relaxation time is greater, the greater the resistance of the medium to rotation of the molecule about this axis, and it is found that a simple reciprocal relation exists between the three relaxation times, Tj, for rotation of each of the axes, and the corresponding rotary diffusion constants defined in equation (i[Pg.138]

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