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A method of constructing programmed motions of a mechanical system

In the paper the method for constructing programmed motion is represented. The requirements for the programmed motion are treated as ideal constraints in analytical mechanics. The programmed motions expressed in lagrange coordinates and in quasi coordinates are investigated. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 3 (46- 57) A METHOD OF CONSTRUCTING PROGRAMMED MOTIONS OF A MECHANICAL SYSTEM Do SANH Hanoi University of Technology ABSTRACT. In the paper the method for constructing programmed motion is represented. The requirements for the programmed motion are treated as ideal constraints in analytical mechanics. The programmed motions expressed in lagrange coordinates and in quasi coordinates are investigated. By applying the form of equations of motion of a constrained mechanical system (7], a schema for calculating programmed motions has been established. By this schema the errors of realizing programmed motions have been reduced and controlled. For illustration of the method some examples have been investigated. §1. Introduction In the theory of controlled motion, there exist some requirements, that restrict the motion of the system under consideration. In other words, the process occurring in this system must satisfy some pre~ set requirements. The conditions, that a process with specified properties the system must realize, are called the programmed and the motion of the system corresponding to this process is named the programmed motion. The problem of programmed motion has been investigated by many authors [2, 8, 9 . ]. In [4, 5] for constructing programmed motion the author•has used the principle of compatibility, which gives an unique point of view for investigating this problem. By this it is possible not only to calculate the needful controlling forces for realizing the given programmed motion, but to find out their construction- this fact serves for qualitative investigations of dynamical processes, for example, stable or optimal investigations, etc, . However, in the mentioned method it can meet errors in realizing programmed motions caused by calculating for example, the inverse of the matrix of inertia. This results the deviation from the required programme and sequently the .