03067nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020003700100024002500137041000800162050001300170072001600183072002300199082001200222100002900234245009600263260003800359264003800397300003400435336002600469337002600495338003600521347002400557505046800581520129201049650001702341650001502358650001702373650002602390650004302416710003402459773002002493776003602513856003802549912001402587942000702601999001302608978-0-306-48682-1DE-He21320141014113427.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803064868219978-0-306-48682-17 a10.1007/b1160202doi aeng 4aTA1-2040 7aTBC2bicssc 7aTEC0000002bisacsh04a6202231 aArdema, Mark D.eauthor.10aAnalytical Dynamicsh[electronic resource] :bTheory and Applications /cby Mark D. Ardema. 1aBoston, MA :bSpringer US,c2005. 1aBoston, MA :bSpringer US,c2005. aXVI, 340 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aReview of Newtonian Dynamics -- Motion and Constraints -- Virtual Displacement and Virtual Work -- Variational Principles -- Generalized Coordinates -- Lagrange’s Equations -- Formulation of Equations -- Integration of Equations -- Examples -- Central Force Motion -- Gyroscopic Motion -- Stability Of Motion -- Impulsive Motion -- Gibbs-Appell Equations -- Hamilton’s Equations -- Contact Transformations -- Hamilton-Jacobi Equation -- Approximation Methods. aIn his great work, Mecanique Analytique (1788)-^Lagrange used the term "analytical" to mean "non-geometrical." Indeed, Lagrange made the following boast: "No diagrams will be found in this work. The methods that I explain in it require neither constructions nor geometrical or mechanical arguments, but only the algebraic operations inherent to a regular and uniform process. Those who love Analysis will, with joy, see mechanics become a new branch of it and will be grateful to me for thus having extended its field." This was in marked contrast to Newton's Philosohiae Naturalis Principia Mathematica (1687) which is full of elaborate geometrical constructions. It has been remarked that the classical Greeks would have understood some of the Principia but none of the Mecanique Analytique. The term analytical dynamics has now come to mean the develop ments in dynamics from just after Newton to just before the advent of relativity theory and quantum mechanics, and it is this meaning of the term that is meant here. Frequent use will be made of diagrams to illus trate the theory and its applications, although it will be noted that as the book progresses and the material gets "more analytical", the number of figures per chapter tends to decrease, although not monotonically. 0aEngineering. 0aVibration.14aEngineering.24aEngineering, general.24aVibration, Dynamical Systems, Control.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978030648681440uhttp://dx.doi.org/10.1007/b116020 aZDB-2-ENG cEB c464d464