On Vector Form of Differential Variational principles of Mechanics

Standard

On Vector Form of Differential Variational principles of Mechanics. / Soltakhanov, Sh. Kh. ; Shugaylo, T. S. ; Yushkov, M. P. .

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 1, 01.01.2018, p. 101-105.

Research output: Contribution to journal › Article › peer-review

Author

Soltakhanov, Sh. Kh. ; Shugaylo, T. S. ; Yushkov, M. P. . / On Vector Form of Differential Variational principles of Mechanics. In: Vestnik St. Petersburg University: Mathematics. 2018 ; Vol. 51, No. 1. pp. 101-105.

BibTeX

@article{7513e27101644e69b43bfac16cbb1ed7,

title = "On Vector Form of Differential Variational principles of Mechanics",

abstract = "We introduce variation of a vector δx which can be interpreted either as a virtual displacement of a system, or as variation of the velocity of a system, or as variation of the acceleration of a system. This vector is used to obtain a unified form of differential variational principles of mechanics from the scalar representative equations of motion. Conversely, this notation implies the original equations of motion, which enables one to consider the obtained scalar products as principles of mechanics. Using the same logical scheme, one constructs a differential principle on the basis of the vector equation of constrained motion of a mechanical system. In this form of notation, it is proposed to conserve the zero scalar products of reactions of ideal constraints and the vector δx. This enables one to obtain also the equations involving generalized constrained forces from this form of notation.",

keywords = "nonholonomic mechanics, linear nonholonomic second order constraints, Lagrange second order equations with multipliers, Maggi equations, generalized Lagrange second order equations with multipliers, generalized Maggi equations, generalized Lagrange second order equations with multipliers, generalized Maggi equations, Lagrange second order equations with multipliers, linear nonholonomic second order constraints, Maggi equations, nonholonomic mechanics",

author = "Soltakhanov, {Sh. Kh.} and Shugaylo, {T. S.} and Yushkov, {M. P.}",

note = "Soltakhanov, S.K., Shugaylo, T.S. & Yushkov, M.P. On Vector Form of Differential Variational Principles of Mechanics. Vestnik St.Petersb. Univ.Math. 51, 101–105 (2018). https://doi.org/10.3103/S1063454118010107",

year = "2018",

month = jan,

day = "1",

doi = "10.3103/S1063454118010107",

language = "English",

volume = "51",

pages = "101--105",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - On Vector Form of Differential Variational principles of Mechanics

AU - Soltakhanov, Sh. Kh.

AU - Shugaylo, T. S.

AU - Yushkov, M. P.

N1 - Soltakhanov, S.K., Shugaylo, T.S. & Yushkov, M.P. On Vector Form of Differential Variational Principles of Mechanics. Vestnik St.Petersb. Univ.Math. 51, 101–105 (2018). https://doi.org/10.3103/S1063454118010107

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We introduce variation of a vector δx which can be interpreted either as a virtual displacement of a system, or as variation of the velocity of a system, or as variation of the acceleration of a system. This vector is used to obtain a unified form of differential variational principles of mechanics from the scalar representative equations of motion. Conversely, this notation implies the original equations of motion, which enables one to consider the obtained scalar products as principles of mechanics. Using the same logical scheme, one constructs a differential principle on the basis of the vector equation of constrained motion of a mechanical system. In this form of notation, it is proposed to conserve the zero scalar products of reactions of ideal constraints and the vector δx. This enables one to obtain also the equations involving generalized constrained forces from this form of notation.

AB - We introduce variation of a vector δx which can be interpreted either as a virtual displacement of a system, or as variation of the velocity of a system, or as variation of the acceleration of a system. This vector is used to obtain a unified form of differential variational principles of mechanics from the scalar representative equations of motion. Conversely, this notation implies the original equations of motion, which enables one to consider the obtained scalar products as principles of mechanics. Using the same logical scheme, one constructs a differential principle on the basis of the vector equation of constrained motion of a mechanical system. In this form of notation, it is proposed to conserve the zero scalar products of reactions of ideal constraints and the vector δx. This enables one to obtain also the equations involving generalized constrained forces from this form of notation.

KW - nonholonomic mechanics, linear nonholonomic second order constraints, Lagrange second order equations with multipliers, Maggi equations, generalized Lagrange second order equations with multipliers, generalized Maggi equations

KW - generalized Lagrange second order equations with multipliers

KW - generalized Maggi equations

KW - Lagrange second order equations with multipliers

KW - linear nonholonomic second order constraints

KW - Maggi equations

KW - nonholonomic mechanics

UR - http://www.scopus.com/inward/record.url?scp=85045107902&partnerID=8YFLogxK

U2 - 10.3103/S1063454118010107

DO - 10.3103/S1063454118010107

M3 - Article

VL - 51

SP - 101

EP - 105

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 14049984