http://espace.library.uq.edu.au/ The University of Queensland en Fez http://blogs.law.harvard.edu/tech/rss http://espace.library.uq.edu.au/view/UQ:194347 The ability to treat vectors in classical mechanics and classical electromagnetism as single geometric objects rather than as a set of components facilitates physical understanding and theoretical analysis. To do the same in four-dimensional spacetime calculations requires a generalization of the vector cross product. Geometric algebra provides such a generalization and is much less abstract than exterior forms. It is shown that many results from geometric algebra are useful for spacetime calculations and can be presented as simple extensions of conventional vector algebra. As an example, it is shown that geometric algebra tightly constrains the possible forms of the self-force that an accelerating charged particle experiences and predicts the Lorentz–Abraham–Dirac equation of motion up to a constant of proportionality. Geometric algebra also makes the important physical content of the Lorentz–Abraham–Dirac equation more transparent than does the standard tensor form of this equation, thus allowing a proposed modification to this equation free from the problems of preacceleration and runaway motion to be easily predicted. 2010-01-31T00:00:00Z Rowland, David R. http://espace.library.uq.edu.au/view/UQ:294624 Introductory discussions of energy transport due to transverse waves on taut strings universally assume that the effects of longitudinal motion can be neglected, but this assumption is not even approximately valid unless the string is idealized to have a zero relaxed length, a requirement approximately met by the slinky spring. While making this additional idealization is probably the best approach to take when discussing waves on strings at the introductory level, for intermediate to advanced undergraduate classes in continuum mechanics and general wave phenomena where somewhat more realistic models of strings can be investigated, this paper makes the following contributions. First, various approaches to deriving the general energy continuity equation are critiqued and it is argued that the standard continuum mechanics approach to deriving such equations is the best because it leads to a conceptually clear, relatively simple derivation which provides a unique answer of greatest generality. In addition, a straightforward algorithm for calculating the transverse and longitudinal waves generated when a string is driven at one end is presented and used to investigate a cos2 transverse pulse. This example illustrates much important physics regarding energy transport in strings and allows the ‘attack waves’ observed when strings in musical instruments are struck or plucked to be approximately modelled and analysed algebraically. Regarding the ongoing debate as to whether the potential energy density in a string can be uniquely defined, it is shown by coupling an external energy source to a string that a suggested alternative formula for potential energy density requires an unphysical potential energy to be ascribed to the source for overall energy to be conserved and so cannot be considered to be physically valid. 2013-03-24T00:09:25Z Rowland, David R. http://espace.library.uq.edu.au/view/UQ:262319 2011-11-27T00:00:00Z Rowland, David R. http://espace.library.uq.edu.au/view/UQ:64312 2007-08-14T00:00:00Z Burke, M. og MacKenzie, M.