Elements of Quaternions
William Rowan Hamilton
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Displaying similar documents to “Lectures on Quaternions”
Elements of Quaternions
GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type
Jean-David Benamou, Philippe Hoch (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
Beyond the edge of certainty : reflections on the rise of physical conventionalism
Helmut Pulte (2000)
Philosophia Scientiae
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Until today, conventionalism is mainly regarded from the point of view of geometry, both in historical as in philosophical perspective. This paper, which corresponds in a certain way with earlier studies of J. Giedymin, aims at a broader interpretation. The importance of the so-called ‘physics of principles’, rooted in the tradition of analytical mechanics, for Poincaré’s conventionalism is emphasized. It is argued that important elements of physical conventionalism can already be found...
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
Piermarco Cannarsa, Giuseppe Da Prato (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
Piermarco Cannarsa, Giuseppe Da Prato (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
A Hamilton-Jacobi approach to junction problems and application to traffic flows
Cyril Imbert, Régis Monneau, Hasnaa Zidani (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to...
Optimal control problems with upper semicontinuous Hamiltonians
Arkadiusz Misztela (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value...
Turnpike theorems by a value function approach
Alain Rapaport, Pierre Cartigny (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness...