Constrained Planar Multibody Systems

The more general case is the constrained, planar system. A constraint is a relation between a subset of the coordinates, which must hold for every possible system configuration. A typical constraint is a joint, which allows motions parallel to certain axes only or restricts certain rotations, e.g. a Kardan joint. More complicated joints are constraints which permit motions only along a prescribed curve or surface. Typical technical examples for this type of joints can be found in contact mechanics, see Sec. 5.5. 

The equations of motion in the constrained case have the form 

the equations of motion for a holonomically constrained system have the structure 

Example 1.3.2 We modify now the truck given in Example 1.3.1 by replacing the spring and damper at the rear end of the loading area by a joint, which allows the loading area to be tilted, cf. Fig. 1.5. The constraint says that the distance between chassis and loading area at the joint s rotation axis must be zero. We must therefore compute the relative vector ps2 between the points of attachment of the joint 52 

Altogether the equations of motion of the constrained truck are given by 

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