國立虎尾科技大學 |

Non-commuting Variations in Mathematics and Physics = A Survey /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Non-commuting Variations in Mathematics and Physics/ by Serge Preston.
Reminder of title:	A Survey /
Author:	Preston, Serge.
Description:	XIV, 235 p. 11 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Vibration. -
Online resource:	https://doi.org/10.1007/978-3-319-28323-4
ISBN:	9783319283234

Non-commuting Variations in Mathematics and Physics = A Survey /
Preston, Serge.

Non-commuting Variations in Mathematics and PhysicsA Survey /[electronic resource] :by Serge Preston. - 1st ed. 2016. - XIV, 235 p. 11 illus.online resource. - Interaction of Mechanics and Mathematics,1860-6245. - Interaction of Mechanics and Mathematics,.

Basics of the Lagrangian Field Theory -- Lagrangian Field Theory with the Non-commuting (NC) Variations -- Vertical Connections in the Congurational Bundle and the NCvariations -- K-twisted Prolongations and -symmetries (by Works of Muriel,Romero -- Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials -- Material Time, NC-variations and the Material Aging -- Fiber Bundles and Their Geometrical Structures, Absolute Parallelism -- Jet Bundles, Contact Structures and Connections on Jet Bundles -- Lie Groups Actions on the Jet Bundles and the Systems of Differential Equations.

This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.

ISBN: 9783319283234

Standard No.: 10.1007/978-3-319-28323-4doiSubjects--Topical Terms:

595749
Vibration.

LC Class. No.: TA355

Dewey Class. No.: 620

Non-commuting Variations in Mathematics and Physics = A Survey /
LDR:03110nam a22004095i 4500 001 973925
003 DE-He213
005 20200704020938.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319283234 $9 978-3-319-28323-4
024 7 $a 10.1007/978-3-319-28323-4 $2 doi
035 $a 978-3-319-28323-4
050 4 $a TA355
050 4 $a TA352-356
072 7 $a TGMD4 $2 bicssc
072 7 $a TEC009070 $2 bisacsh
072 7 $a TGMD $2 thema
082 0 4 $a 620 $2 23
100 1 $a Preston, Serge. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1106884
245 1 0 $a Non-commuting Variations in Mathematics and Physics $h [electronic resource] : $b A Survey / $c by Serge Preston.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XIV, 235 p. 11 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Interaction of Mechanics and Mathematics, $x 1860-6245
505 0 $a Basics of the Lagrangian Field Theory -- Lagrangian Field Theory with the Non-commuting (NC) Variations -- Vertical Connections in the Congurational Bundle and the NCvariations -- K-twisted Prolongations and -symmetries (by Works of Muriel,Romero -- Applications: Holonomic and Non-Holonomic Mechanics,H.KleinertAction Principle, Uniform Materials,and the Dissipative Potentials -- Material Time, NC-variations and the Material Aging -- Fiber Bundles and Their Geometrical Structures, Absolute Parallelism -- Jet Bundles, Contact Structures and Connections on Jet Bundles -- Lie Groups Actions on the Jet Bundles and the Systems of Differential Equations.
520 $a This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equations with dissipation and corresponding s balance laws is presented.
650 0 $a Vibration. $3 595749
650 0 $a Dynamical systems. $3 1249739
650 0 $a Dynamics. $3 592238
650 0 $a Mathematical physics. $3 527831
650 0 $a Mechanics. $3 527684
650 1 4 $a Vibration, Dynamical Systems, Control. $3 670825
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
650 2 4 $a Classical Mechanics. $3 1140387
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319283210
776 0 8 $i Printed edition: $z 9783319283227
830 0 $a Interaction of Mechanics and Mathematics, $x 1860-6245 $3 1268837
856 4 0 $u https://doi.org/10.1007/978-3-319-28323-4
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)