000 04121nam a22005175i 4500
001 978-0-387-28316-6
003 DE-He213
005 20170628033254.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387283166
_9978-0-387-28316-6
024 7 _a10.1007/0-387-28316-1
_2doi
050 4 _aTJ1-1570
072 7 _aTGB
_2bicssc
072 7 _aTEC009070
_2bisacsh
082 0 4 _a621
_223
100 1 _aHowland, R. A.
_eauthor.
245 1 0 _aIntermediate Dynamics: A Linear Algebraic Approach
_h[electronic resource] /
_cby R. A. Howland ; edited by Frederick F. Ling, William Howard Hart.
264 1 _aBoston, MA :
_bSpringer US,
_c2006.
300 _aXX, 542 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMechanical Engineering Series,
_x0941-5122
505 0 _aLinear Algebra -- Prologue -- Vector Spaces -- Linear Transformations on Vector Spaces -- Special Case—Square Matrices -- Epilogue -- 3-D Rigid Body Dynamics -- Prologue -- Kinematics -- Kinetics -- Epilogue -- Analytical Dynamics -- Prologue -- Analytical Dynamics: Perspective -- Lagrangian Dynamics: Kinematics -- Lagrangian Dynamics: Kinetics -- Integrals of Motion -- Hamiltonian Dynamics -- Epilogue.
520 _aAs the name implies, Intermediate Dynamics: A Linear Algebraic Approach views "intermediate dynamics"--Newtonian 3-D rigid body dynamics and analytical mechanics--from the perspective of the mathematical field. This is particularly useful in the former: the inertia matrix can be determined through simple translation (via the Parallel Axis Theorem) and rotation of axes using rotation matrices. The inertia matrix can then be determined for simple bodies from tabulated moments of inertia in the principal axes; even for bodies whose moments of inertia can be found only numerically, this procedure allows the inertia tensor to be expressed in arbitrary axes--something particularly important in the analysis of machines, where different bodies' principal axes are virtually never parallel. To understand these principal axes (in which the real, symmetric inertia tensor assumes a diagonalized "normal form"), virtually all of Linear Algebra comes into play. Thus the mathematical field is first reviewed in a rigorous, but easy-to-visualize manner. 3-D rigid body dynamics then become a mere application of the mathematics. Finally analytical mechanics--both Lagrangian and Hamiltonian formulations--is developed, where linear algebra becomes central in linear independence of the coordinate differentials, as well as in determination of the conjugate momenta. Features include: o A general, uniform approach applicable to "machines" as well as single rigid bodies. o Complete proofs of all mathematical material. Similarly, there are over 100 detailed examples giving not only the results, but all intermediate calculations. o An emphasis on integrals of the motion in the Newtonian dynamics. o Development of the Analytical Mechanics based on Virtual Work rather than Variational Calculus, both making the presentation more economical conceptually, and the resulting principles able to treat both conservative and non-conservative systems.
650 0 _aEngineering.
650 0 _aEngineering mathematics.
650 0 _aVibration.
650 0 _aMechanical engineering.
650 1 4 _aEngineering.
650 2 4 _aMechanical Engineering.
650 2 4 _aVibration, Dynamical Systems, Control.
650 2 4 _aNumerical and Computational Methods in Engineering.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
700 1 _aLing, Frederick F.
_eeditor.
700 1 _aHart, William Howard.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387280592
830 0 _aMechanical Engineering Series,
_x0941-5122
856 4 0 _uhttp://dx.doi.org/10.1007/0-387-28316-1
912 _aZDB-2-ENG
999 _c14422
_d14422