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Extra info for An introduction to the theory of superfluidity
63) The total forces in x,y,z-directions become (F ,F ,F ) = x y z JJ Contact (PI' P2 cos 0: - P3 sin 0:, P2 sin 0: + P3 cos 0:) For concentrated contacts, 0: is a constant. 13; a practical example is a flanging railway wheel. dxdy . 64 ) 0:, see Fig. We finish this subsection by considering the potential contact region A . 56h). Also, many algorithms need an estimate of the contact; this leads to fewer iterations because the initial estimate is better. Here we will give a general expression for this estimate A , which is sharp in the sense that it cannot be improved without C specifying the geometry.
69) The procedure for finding A , if F . is prescribed, reads c I. 2. 3. 4. 5. 69); goto "3" c Else: READY. 70) "4" 40 z = true means doing an entire calculation all over again. 3 FRICTIONAL BOUNDARY CONDITIONS FOR BODIES OF REVOLUTION WITH THE AXES ALMOST IN ONE PLANE Consider a typical situation, such as given in Fig. 5. Let l be the z-coordinate of the a center of curvature in x-direction at the origin of the coordinate system, which lies in the contact area. 71) The bodies are rotated about these centers with angular velocities W (W ,W ,W ), so .
IJ I,J J,l which is used in linear elasticity to describe the deformation. Also, in the sequel, we will use the smallness of the displacement gradients direct1y. Note that there are 9 displacement gradients and only 6 strains, so that the smallness of the strains does not imply the smallness of the displacement gradients. The converse is true, of course. In the above we assumed a new reference state at every instant of time. One can also attach a reference state to each body separately. These unstressed states coincide with the rigid fields induced by the axles.