Accession Number:

ADA561412

Title:

A Pseudo-Reversing Theorem for Rotation and its Application to Orientation Theory

Descriptive Note:

Technical rept.

Corporate Author:

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION EDINBURGH (AUSTRALIA)

Personal Author(s):

• Koks, Don

Report Date:

2012-03-01

Pagination or Media Count:

53.0

Abstract:

We state and prove a useful theorem on manipulating rotation order which, while not new, is barely present in the literature. This theorem allows the order of a sequence of rotations to be reversed, provided that the sense of the axes of rotation is changed from body to space fixed or vice versa. We use the theorem to aid calculations in geodesy constructing a local northeastdown coordinate system and aerospace theory relating yawpitchroll rates to vehicle angular velocity. The new notation here sheds light generally on the field of orientation theory, as well as giving insight to standard terms relating to wind direction used for treating ship motion. Although we present our analyses in the style of a tutorial in the general subject of spatial orientation theory, there is new notation here, along with alternative and novel ways of treating problems that are often seen as difficult or obscure by practitioners. This report follows on from the 2005 DSTO report DSTOTN0640, but is completely self contained, and DSTOTN0640 need not be read beforehand.

Descriptors:

• *ORIENTATION(DIRECTION)
• *ROTATION
• *THEOREMS
• AEROSPACE SYSTEMS
• ANGULAR MOTION
• AUSTRALIA
• COORDINATES
• SHIP MOTION
• SPACE NAVIGATION
• VELOCITY
• WIND DIRECTION
• YAW

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE