Skip to main content Accessibility help
×
Hostname: page-component-788cddb947-xdx58 Total loading time: 0 Render date: 2024-10-12T03:05:45.928Z Has data issue: false hasContentIssue false

Epilogue

Published online by Cambridge University Press:  05 October 2014

Pierre T. Kabamba
Affiliation:
University of Michigan, Ann Arbor
Anouck R. Girard
Affiliation:
University of Michigan, Ann Arbor
Get access

Summary

During this 10-chapter journey through Fundamentals of Aerospace Navigation and Guidance, the book endeavors to give an orderly account of the lay of this land. This orderliness should now be apparent through synergies between many items. By this we mean that, often, a newly introduced fundamental relies on past fundamentals, sheds new light on some of them, and foreshadows future ones. Let us give examples of such synergies.

  1. Inequality (1.2) establishes that, in static systems, good navigation combined with good navigation-based guidance guarantees good guidance. This principle is extended to deterministic linear dynamic systems through inequality (7.54) under the umbrella of the deterministic separation principle. Then, it is further extended to systems with linear dynamics, quadratic cost, and Gaussian noise processes in Section 9.5.6 under the umbrella of the stochastic separation principle.

  2. The controllability Gramian is introduced in Proposition 2.22 to settle the binary question of controllability of a state. However, after deriving optimization results in Section 8.4 and extending them to optimal control in Section 9.3, we show in Example 9.6 that the same controllability Gramian can also be used as a quantitative measure of controllability through (9.54).

  3. The implicit function theorem, introduced in Section 6.3 to analyze the accuracy of ballistic shots, is also used in Proposition 8.6 to establish the existence of Lagrange multipliers in constrained optimization. This result is extended in Sections 8.4 and 9.3 to establish the existence of the time varying co-state vector.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

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.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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.

  • Epilogue
  • Pierre T. Kabamba, University of Michigan, Ann Arbor, Anouck R. Girard, University of Michigan, Ann Arbor
  • Book: Fundamentals of Aerospace Navigation and Guidance
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107741751.012
Available formats
×

Save book to Dropbox

To save content items to your account, please 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 account. Find out more about saving content to Dropbox.

  • Epilogue
  • Pierre T. Kabamba, University of Michigan, Ann Arbor, Anouck R. Girard, University of Michigan, Ann Arbor
  • Book: Fundamentals of Aerospace Navigation and Guidance
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107741751.012
Available formats
×

Save book to Google Drive

To save content items to your account, please 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 account. Find out more about saving content to Google Drive.

  • Epilogue
  • Pierre T. Kabamba, University of Michigan, Ann Arbor, Anouck R. Girard, University of Michigan, Ann Arbor
  • Book: Fundamentals of Aerospace Navigation and Guidance
  • Online publication: 05 October 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107741751.012
Available formats
×