By J. M. Skowronski
ISBN-10: 012648130X
ISBN-13: 9780126481303
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Extra resources for Control Dynamics of Robotic Manipulators
Example text
The investigation exercised on this remaining part of Jtf, that is, over C A is called the study in the large. 2. 1, extending it now to the surface J f , the latter defined by H(q,q) = \q 2 + ^Q (q)dq P = \q 2 + \aq 2 + ±bq* + ±cq . , q . 1). 13) 6 and it encloses not only A but also three disjoint A#, the basic A inclusive. 31 corresponding to it is the highest of the system on A so H = 3 A , and the complement of sets enclosed by this curve is the region in the large C A that underlies the cup in the large.
3'). Here we denote RQ = [ t , o o ) c R . Later we may also need R { , = [t ,t \ where t < oo is a terminal instant. N o w the solutions do depend upon the initial instant £ , and the corresponding curves in ft are called motions. 3') and even a dynamical system in ft, but when projected down to A exhibits none of the nice properties of the a u t o n o m o u s system. The motions are not unique there; that is, they may intersect. However, the vector / ( x , m, t) is obviously still tangent to the motion and forms a vector field with singularities.
21) J where 6 5 0 , Q! are matrices that agree with the matrix A(q) but for the ith column which is replaced by the vectors Q a n d Q \ respectively. The example below illustrates the above notation on the case of 3 D O F system which is subject t o the spring forces only in order t o concentrate on o u r present problem. 1. 1 P O T E N T I A L FORCES. £(#, — q ) = 0. A63/93 -
Control Dynamics of Robotic Manipulators by J. M. Skowronski
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