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- Title
An Alternative Proof of Euler's Rotation Theorem.
- Authors
Joseph, Toby
- Abstract
The value of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi></math> ht can vary between 0 and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi> </mi></mrow></math> ht . To prove this, imagine we had chosen a different point HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mn>1</mn></msub></math> ht instead of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> ht for translation. In fact, the displacing points (such as HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mn>1</mn></msub></math> ht ) themselves need not form part of the rigid body. It may be that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">F</mi></math> ht is not parallel to HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>n</mi><mo stretchy="false">^</mo></mover></math> ht .
- Subjects
EULER theorem; RIGID body mechanics; EULER angles; EVIDENCE; EULER equations (Rigid dynamics); FIXED point theory
- Publication
Mathematical Intelligencer, 2020, Vol 42, Issue 4, p44
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-020-09991-z