The genesis of this paper lies in theoretical questions in kinematics where a central role is played by naturally occurring families of rigid motions of 3-space. The resulting trajectories are parametrized families of space curves, and it is important to understand the generic singularities they can exhibit. For practical purposes one seeks to classify germs of space curves of fairly small Ae-codimension. It is however little harder to list the A-simple germs, which includes all germs of Ae-codimension ≤11: that then is the principal objective of this paper.
Local models are given for the singularities which can appear on the trajectories of general one-dimensional motions of the plane or space. Versal unfoldings of these model singularities give simple pictures describing the family of trajectories arising from small deformations of the tracing point.
The A -classification of multigerm singularities is discussed, based on the theory of complete transversals. An A -classification of r-multigerms from the plane to 3-space of A -codimension ≤ 6 − r is carried out and the bifurcation geometry of these singularities analysed. This work has applications to the study of two-dimensional spatial motions, giving local models for the singularities which appear on general trajectories of rigid body motions from the plane to 3-space. In addition, our classification is extensive enough to give the full list of simple multigerm singularities from the plane to 3-space.
C A (2000) An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives. Computer physics communications, 132 (1-2). pp. 142-165.
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