TY - CHAP

T1 - Linear transformation of forces

AU - Soltakhanov, Shervani Kh

AU - Yushkov, Mikhail P.

AU - Zegzhda, Sergei A.

N1 - Copyright: Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - In this Chapter the linear transformation of forces is introduced. In this case for holonomic systems the notion of ideal constraints and the relation for virtual elementary work are applied. By the transformation of forces, Lagrange's equations of the first and second kinds are obtained. The theorem of holonomic mechanics is formulated by which the given motion over the given curvilinear coordinate can be provided by an additional generalized force corresponding to this coordinate. For nonholonomic systems the linear transformation of forces is introduced applying Chetaev's postulates. In this case with the help of generalized forces, corresponding to the equations of constraints, the family of fundamental equations of the nonholonomic mechanics is obtained in compact form. The theorem of holonomic mechanics is formulated according to which the given change of quasivelocity can be provided by one additional force corresponding to this quasivelocity. The application of the formulated theorems of the holonomic and nonholonomic mechanics is demonstrated on the example of the solution of two problems on the controllable motion connected with the flight dynamics. At the end of this chapter the linear transformation of forces is used to obtain the Gauss principle.

AB - In this Chapter the linear transformation of forces is introduced. In this case for holonomic systems the notion of ideal constraints and the relation for virtual elementary work are applied. By the transformation of forces, Lagrange's equations of the first and second kinds are obtained. The theorem of holonomic mechanics is formulated by which the given motion over the given curvilinear coordinate can be provided by an additional generalized force corresponding to this coordinate. For nonholonomic systems the linear transformation of forces is introduced applying Chetaev's postulates. In this case with the help of generalized forces, corresponding to the equations of constraints, the family of fundamental equations of the nonholonomic mechanics is obtained in compact form. The theorem of holonomic mechanics is formulated according to which the given change of quasivelocity can be provided by one additional force corresponding to this quasivelocity. The application of the formulated theorems of the holonomic and nonholonomic mechanics is demonstrated on the example of the solution of two problems on the controllable motion connected with the flight dynamics. At the end of this chapter the linear transformation of forces is used to obtain the Gauss principle.

UR - http://www.scopus.com/inward/record.url?scp=67049098662&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85847-8_3

DO - 10.1007/978-3-540-85847-8_3

M3 - Chapter

AN - SCOPUS:67049098662

SN - 9783540858461

T3 - Foundations in Engineering Mechanics

SP - 77

EP - 103

BT - Mechanics of non-holonomic systems

A2 - Soltakhanov, Shervani

A2 - Zegzhda, Sergei

A2 - Yushkov, Mikhail

ER -