Welcome to the NavList Message Boards.

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    or...
       
    Reply
    Re: Applications of Complex Analysis to Celestial Navigation
    From: Robin Stuart
    Date: 2009 Oct 26, 16:53 -0700

    John,
    
    You may have seen the paper by now but if not let me explain that the method 
    does not make use trigonometric functions with complex arguments but just 
    simple arithmetic operations on complex numbers. In a certain sense it is 
    analogous to the use of complex numbers in AC circuit analysis. A point on 
    the surface of a sphere is identified with a complex number by stereographic 
    projection. A single complex number encapsulates both of the angular 
    coordinates (e.g. latitude/longitude, declination/GHA or altitude/azimuth). 
    If z is a complex number representing the declination & GHA of a celestial 
    body and w is a complex number representing its altitude & azimuth then the 
    two are related by
     
    w = ( a * z + b ) / ( -Conjugate[b] * z + Conjugate[a] )
     
    where a and b are complex numbers that depend only on the latitude and 
    longitude of the observer. Altitude and azimuth are computed simultaneously 
    by a single equation.
     
    As far as Andres' referring to quaternions as a special case of tensor 
    calculus, I took that to mean that the algebra of quaternions is isomorphic 
    to that of the Pauli matrices. I would hesitate to place quaternions on the 
    same level as complex numbers however. The latter, of course, give rise to 
    the whole field of complex function analysis which is not really replicated 
    for quaternions,
    
    Robin Stuart
    
    
    --~--~---------~--~----~------------~-------~--~----~
    NavList message boards: www.fer3.com/arc
    Or post by email to: NavList@fer3.com
    To unsubscribe, email NavList+unsubscribe@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
    Email:

    Email Settings

    Posting Code:

    Custom Index

    Subject:
    Author:
    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site