2-D KCL, WNLRT and SRT

Prasad, Phoolan

doi:10.1007/978-981-10-7581-0_8

Phoolan Prasad²

Part of the book series: Infosys Science Foundation Series ((ISFM))

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Abstract

In this chapter we first review the equations of 2-D KCL, WNLRT and SRT. Then we review their important properties and solutions.

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Notes

1.
Care is required when we are talking of \((\xi , t)\)-plane, which is the same as (x, y)-plane and not to be confused with 3-D (x, y, t)-space.
2.
Derivation is simple. In the jump relations, we collect all terms containing \(\theta _\ell \) on the left-hand side and those containing \(\theta _r\) on the right-hand side. Then, we square and add the two jump relations to get (8.39).
3.
Derivation requires multiplying the first jump relation in (8.36) by \(\cos \theta _\ell \), the second by \(\sin \theta _\ell \) and adding. Then we get \(Sg_r \sin (\theta _\ell -\theta _r) +m_r \cos (\theta _\ell -\theta _r) - m_\ell = 0\), in which we use (8.38) to get (8.40).
4.
Neglecting the image of a contact discontinuity which have been removed by a proper choice of \(\xi \).

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Department of Mathematics, Indian Institute of Science, Bengaluru, Karnataka, India
Phoolan Prasad

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Phoolan Prasad
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Correspondence to Phoolan Prasad .

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Prasad, P. (2017). 2-D KCL, WNLRT and SRT. In: Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-10-7581-0_8

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DOI: https://doi.org/10.1007/978-981-10-7581-0_8
Published: 07 March 2018
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-7580-3
Online ISBN: 978-981-10-7581-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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