GAUSS CONSTRAINT AS A FUNCTION OF ACCELERATION AND VELOCITY

• Published in: Bulletin de l'Académie serbe des sciences, Classe des sciences mathématiques et naturelles. Sciences mathématiques no. 17; pp. 27 - 32
• Main Authors: LUKAČEVIĆ, MIRJANA M., ČOVIĆ, V. M.
• Format: Journal Article
• Language: English
• Published: Académie Serbe des Sciences et des Arts 01-01-1989
• Subjects: Differential equations; Kinetics; Mathematical functions; Mathematical vectors; Mechanical systems; Tensors; Velocity
• ISSN: 0561-7332; 2406-0909

The motion of a non-holonomic rheonomic system of N material points is considered as the motion of a constrained representative point in the 3N-dimensional euclidian space. Starting from the condition of extremality of the Gauss constraint, treated as a function not only of the acceleration, but also of the velocity of the representative point, one obtains the relation from which follow the differential equations of system's motion and the reactions of the ideal constraints to which this motion is subject. Finally, one concludes that the reactions of the ideal constraints of the mechanical system can be explicitly found from the stationarity condition of the Gauss constraint only using a mode of variation more free than the one applied in Gauss principle, i. e., substituing the Gauss mode of variation by the Jourdain's one.