{"product_id":"higher-order-differential-equations-and-elasticity-paperback-softback","title":"Higher-Order Differential Equations and Elasticity - Paperback \/ softback","description":"\u003cp\u003eHigher-Order Differential Equations and Elasticity is the third book within \u003ci\u003eOrdinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. \u003c\/i\u003eAs a set, they are the fourth volume in the series \u003ci\u003eMathematics and Physics Applied to Science and Technology\u003c\/i\u003e. This third book consists of two chapters (chapters 5 and 6 of the set).\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e \u003cbr\u003e\u003cbr\u003e\u003cli\u003eDiscusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves\u003c\/li\u003e \u003cbr\u003e\u003cbr\u003e\u003cli\u003ePresents differential equations of the second and higher order, including non-linear and with variable coefficients\u003c\/li\u003e \u003cbr\u003e\u003cbr\u003e\u003cli\u003eCompares relation of differentials with the principles of thermodynamics\u003c\/li\u003e \u003cbr\u003e\u003cbr\u003e\u003cli\u003eDescribes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates\u003c\/li\u003e \u003cbr\u003e\u003cbr\u003e\u003cli\u003ePresents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates\u003c\/li\u003e \u003c\/ul\u003e","brand":"Taylor \u0026 Francis","offers":[{"title":"Default Title","offer_id":45584271802606,"sku":"9781032653730","price":77.59,"currency_code":"AUD","in_stock":true}],"url":"https:\/\/bookland.com.au\/products\/higher-order-differential-equations-and-elasticity-paperback-softback","provider":"Book Land AU","version":"1.0","type":"link"}