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Extension to eulers's theorem to n-dimensional spaces
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Bar-Itzhack, Itzhack Y. |
| Copyright Year | 1989 |
| Description | Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given in this paper and proven in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular-velocity which, when applied to the initial orientation, yields eventually the final orientation regardless of what angular velocity generated the latter. Finally, the extension of the theorem is demonstrated in a four-dimensional numerical example. |
| File Size | 535499 |
| Page Count | 18 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19900004115 |
| Archival Resource Key | ark:/13960/t2h759v7m |
| Language | English |
| Publisher Date | 1989-10-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Attitude Inclination Rigid Structures Euclidean Geometry Theorems Algorithms Vectors Mathematics Mathematical Models Angular Velocity Rotation Three Dimensional Models Gyration Matrices Mathematics Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
