By Isaac M. Khalatnikov, Isaac Markovich Khalatnikov
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Extra info for An introduction to the theory of superfluidity
As mentioned earlier, the apparent disadvantages are their large number and the difficulty to be adapted for particular topologies such as open kinematic chains. 1. Planar Multibody Systems 25 contiguous elements. With these coordinates the motion of each element is defined regardless of the motion of the rest of them. However, the motion of the adjacent elements, linked by a kinematic joint, cannot be arbitrary. Rather it must generate a relative motion between these elements according to the nature of the joint.
However, they pay the price as the number of coordinates is increased (seven instead of six for each element). There is also the additional problem of having to take into account the constraint equation that relates the four parameters . The simplest and easiest to understand of the four-parameter systems is that which defines the orientation of the moving frame by means of a rotation angle ψ around an axis defined by the three direction cosines of the unit vector u. 21). 4) In practice, the four-parameter system used the most is not the one suggested, but one made up of the so-called Euler parameters, that is closely related to the former.
In regard to the rigid body constraints of elements defined by more than two basic points, there are a few particular cases that should be analyzed in detail. 16 shows three elements with more than two basic points in each one of them. 1. 16. Different types of elements with more than two basic points. 16b where the three points are aligned. In principle, the three equations (i)-(iii) could also be valid in this case. It can be realized that they are not independent and therefore are not capable of guaranteeing that the element will move as a rigid body.
An introduction to the theory of superfluidity by Isaac M. Khalatnikov, Isaac Markovich Khalatnikov