The Functional Gradient Description Method of Space Coordinate Transformation

doi:10.13485/j.cnki.11-2089.2014.0145

Abstract

Abstract:

This?study?proposes?the?conception?of?coordinate?transformation?gradient?field,?which?can?realize?the?space?coordinate?transformation?from?small?angle?to?arbitrary?angle?and?from?static?to?dynamical.?

Based?on?the?equivalent?of?the?unit?quaternion?rotation?matrix?and?the?Rodrigo?matrix,?this?paper?reveals?the?mathematical?relationship?between?the?spatial?coordinate?transformation?and?the?functional?

gradient?and?derives?an?arbitrary?coordinate?transformation?formula?expressed?by?functional?gradient?in?space.?The?results?indicate?that?the?essence?of?spatial?coordinate?transformation?is?potential?field

?in?mathematic?and?we?can?unify?all?the?space?coordinate?transformations?by?using?the?conception?of?field,?which?is?the?theoretical?foundation?for?the?further?study?of?time?continuous?space?coordinate

?transformation?and?this?study?also?gives?a?new?solution?for?the?attitude?determination?of?motion?carriers.

Key words: spatial coordinate transformation, functional gradient field, complete equivalence, field

CLC Number:

P207

DUAN Pengshuo LIU Gengyou GONG Youliang HAO Xiaoguang WANG Nazi. The Functional Gradient Description Method of Space Coordinate Transformation[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(10): 1005-1012.

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