Simultaneous Systems of Differential Equations and Multi-dimensional Oscillators Mathematics and Physics for Science and Technology Series
Auteur : Braga da Costa Campos Luis Manuel
Simultaneous Differential Equations and Multidimensional Vibrations is the fourth 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 fourth book consists of two chapters (chapters 7 and 8 of the set).
The first chapter concerns simultaneous systems of ordinary differential equations and focuses mostly on the cases that have a matrix of characteristic polynomials, namely linear systems with constant or homogeneous power coefficients. The method of the matrix of characteristic polynomials also applies to simultaneous systems of linear finite difference equations with constant coefficients.
The second chapter considers linear multi-dimensional oscillators with any number of degrees of freedom including damping, forcing, and multiple resonance. The discrete oscillators may be extended from a finite number of degrees-of-freedom to infinite chains. The continuous oscillators correspond to waves in homogeneous or inhomogeneous media, including elastic, acoustic, electromagnetic, and water surface waves. The combination of propagation and dissipation leads to the equations of mathematical physics.
- Presents simultaneous systems of ordinary differential equations and their elimination for a single ordinary differential equation
- Includes cases with a matrix of characteristic polynomials, including simultaneous systems of linear differential and finite difference equations with constant coefficients
- Covers multi-dimensional oscillators with damping and forcing, including modal decomposition, natural frequencies and coordinates, and multiple resonance
- Discusses waves in inhomogeneous media, such as elastic, electromagnetic, acoustic, and water waves
- Includes solutions of partial differential equations of mathematical physics by separation of variables leading to ordinary differential equations
Superior Tecnico (IST) of Lisbon Technical University. His tutorials as a student (1970) were
followed by a career at the same institution (IST) through all levels: Assistant (1972), Assistant
with tenure (1974), Assistant Professor (1978), Associate Professor (1982), Chair de Applied
Mathematics and Mechanics (1985). He has been coordinator of undergraduate and post-graduate
degrees in Aerospace Engineering since their creation in 1991. He is also coordinator of the
Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and
director and founder of the Center for Aeronautical and Space Science and Technolo
Date de parution : 11-2019
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