000			03042 a2200253 4500
003			OSt
005			20230801114250.0
008			230721b xxu||||| |||| 00| 0 eng d
020			_a9780367137205
040			_cIIT Kanpur
041			_aeng
082			_a531.3820151535 _bC157h
100			_aCampos, L. M. B. C
245			_aHigher-order differential equations and elasticity [Vol.IV Book 6] _bordinary differential equations with applications to trajectories and oscillations _cL. M. B. C Campos
260			_bCRC Press _c2020 _aBoca Raton
300			_axxix, 363p
440			_aMathematics and physics for science and technology
490			_a/ edited by L. M. B. C Campos
520			_aHigher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic. Discusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves Presents differential equations of the second and higher order, including non-linear and with variable coefficients Compares relation of differentials with the principles of thermodynamics Describes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates Presents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates
650			_aElasticity -- Mathematical models
650			_aThermoelasticity -- Mathematical models
650			_aDifferential equations
942			_cBK
999			_c566675 _d566675