Download e-book for iPad: Nonlinear Ordinary Differential Equations: Problems and by D. W. Jordan

By D. W. Jordan

ISBN-10: 0199212031

ISBN-13: 9780199212033

An excellent significant other to the hot 4th version of Nonlinear traditional Differential Equations through Jordan and Smith (OUP, 2007), this article comprises over 500 difficulties and fully-worked suggestions in nonlinear differential equations. With 272 figures and diagrams, matters coated comprise section diagrams within the aircraft, type of equilibrium issues, geometry of the section airplane, perturbation tools, compelled oscillations, balance, Mathieu's equation, Liapunov tools, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's method.The difficulties are of variable trouble; a few are regimen questions, others are longer and extend on options mentioned in Nonlinear traditional Differential Equations 4th version, and regularly could be tailored for coursework or self-study.Both texts disguise a large choice of functions whereas holding mathematical prequisites to a minimal making those a great source for college kids and teachers in engineering, arithmetic and the sciences"

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Nonlinear Ordinary Differential Equations: Problems and - download pdf or read online

An excellent better half to the recent 4th version of Nonlinear usual Differential Equations through Jordan and Smith (OUP, 2007), this article comprises over 500 difficulties and fully-worked options in nonlinear differential equations. With 272 figures and diagrams, topics lined contain part diagrams within the airplane, class of equilibrium issues, geometry of the section aircraft, perturbation equipment, pressured oscillations, balance, Mathieu's equation, Liapunov tools, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's process.

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Additional info for Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers

Example text

The behaviour of the bob is as follows: • 0 < c < mg(a − h)3 /h. There are two equilibrium positions: the bob vertically below the suspension point which is a stable centre, or the bob above which is an unstable saddle, • c takes the intermediate values defined by (iii). Both the highest and lowest points becomes a saddles. The inclined equilibrium points are centres. • c > mg(a + h)3 /h. The lowest point remains a saddle but the highest point switches back to a saddle. 33 A pendulum with equation x¨ + sin x = 0 oscillates with amplitude a.

18. 19 If a bead slides on a smooth parabolic wire rotating with constant angular velocity ω about a vertical axis, then the distance x of the particle from the axis of rotation satisfies (1 + x 2 )x¨ + (g − ω2 + x˙ 2 )x = 0. Analyse the motion of the bead in the phase plane. 19. The differential equation of the bead is (1 + x 2 )x¨ + (g − ω2 + x˙ 2 )x = 0. The equation represents the motion of a bead sliding on a rotating parabolic wire with its lowest point at the origin. The variable x represents distance from the axis of rotation.

41. Let the distance between the supports be 2a, and let the origin be at the hinge with horizontal and vertical axes. The supports have coordinates (a, L) and (−a, L). The potential energy includes contributions from the height of the bob and the springs. We assume that the springs obey Hooke’s law which states that potential energy = 12 (stiffness) × (extension)2 . Therefore the potential energy is √ V (θ ) = 12 mgL cos θ − 12 mgL + 12 k{ [(a − L sin θ )2 + (L − L cos θ )2 ] − a}2 √ + 12 k{ [(a + L sin θ)2 + (L − L cos θ )2 ] − a}2 defined so that V (0) = 0.

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Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers by D. W. Jordan


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