Skip to main content Accessibility help
×
Home
Hostname: page-component-cf9d5c678-7bjf6 Total loading time: 0.7 Render date: 2021-08-06T01:42:41.119Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Note on Whitham's ‘The propagation of weak spherical shocks in stars’

Published online by Cambridge University Press:  24 October 2008

D. S. Jones
Affiliation:
Department of MathematicsUniversity of Manchester

Extract

In his paper on ‘The propagation of weak spherical shocks in stars’ Whitham(1) uses as the basis of his non-linear theory the solution of the linear equation

where the suffixes denote partial derivatives and A, B, C are functions of r only. In obtaining his solution he assumes (i) that

where ξ = t – ∫dr/A and fn(ξ) is the nth integral of f with respect to ξ, and (ii) that the function f may be identified with the corresponding function which occurs when gravity is neglected, i.e. when A becomes the constant A0, B = −2/r and C = 0. Having assumed that (2) exists, Whitham is able to show that it will hold asymptotically for Aξ/r ≪ 1 and A′ = O (A/r).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

(1)Whitham, G. B.Commun. pure appl. Math. 6 (1953), 397414.CrossRefGoogle Scholar

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Note on Whitham's ‘The propagation of weak spherical shocks in stars’
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Note on Whitham's ‘The propagation of weak spherical shocks in stars’
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Note on Whitham's ‘The propagation of weak spherical shocks in stars’
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *