Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula

    134983_134983.pdf (142.7Kb)
    Access Status
    Open access
    Authors
    Thomas, C.
    Featherstone, Will
    Date
    2005
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Thomas, C. and Featherstone, W. 2005. Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula. Journal of Surveying Engineering. 131 (1): pp. 20-26.
    Source Title
    Journal of Surveying Engineering
    DOI
    10.1061/(ASCE)0733-9453(2005)131:1(20)
    ISSN
    07339453
    School
    Department of Spatial Sciences
    URI
    http://hdl.handle.net/20.500.11937/36501
    Collection
    • Curtin Research Publications
    Abstract

    Vincenty’s (1975) formulas for the direct and inverse geodetic problems (i.e., in relation to the geodesic) have been verified by comparing them with a new formula developed by adapting a fourth-order Runge-Kutta scheme for the numerical solution of ordinary differential equations, advancing the work presented by Kivioja in 1971. A total of 3,801 lines of varying distances (10 to 18,000km) and azimuths (0 to 90°, because of symmetry) were used to compare these two very different techniques for computing geodesics. In every case, the geodesic distances agreed to within 0.115mm, and the forward and reverse azimuths agreed to within 5 × 10 −6 seconds of arc, thus verifying Vincenty’s formula. If one wishes to plot the trajectory of the geodesic, however, the fourth-order Runge-Kutta extension of Kivioja’s formula is recommended as a numerically efficient and convenient approach.

    Related items

    Showing items related by title, author, creator and subject.

    • A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact
      Cui, Lei; Dai, J. (2010)
      This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic ...
    • Why did the apple fall? A new model to explain Einstein's gravity
      Stannard, W.; Blair, D.; Zadnik, Marjan; Kaur, T. (2017)
      © 2016 IOP Publishing Ltd. Newton described gravity as an attractive force between two masses but Einstein's General Theory of Relativity provides a very different explanation. Implicit in Einstein's theory is the idea ...
    • Geometric Kinematics of Point Contact
      Cui, Lei; Dai, J. S. (2010)
      This paper applies Darboux frame method to developing geometric kinematics of sliding-spin-rolling motion of rigid objects with point contact. For the first time, the geodesic curvatures, normal curvatures and geodesic ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.