Harmonic Analysis on So(3)
نویسنده
چکیده
Such a rotation g can be described by three parameters. For instance, if you know the axis of rotation (specified by a direction or a point on S or two angles) and the angle of rotation (one parameter), g is determined uniquely. Alternatively, a matrix g ∈ R3×3 has 9 entries, but the requirement that gg = 1 gives 6 conditions on these entries, and again 9− 6 = 3. (The condition that det g = 1 singles out one half of the matrices satisfying gg = 1; it does not reduce the dimension.) Summarizing in fancy language and adding some precision, we have:
منابع مشابه
Dynamic Harmonic Analysis of Long Term over Voltages Based on Time Varying Fourier series in Extended Harmonic Domain
Harmonics have become an important issue in modern power systems. The widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs an Extended Harmonic Domain (EHD) based framework for dynamic analysis of long term analysis over voltages during the tra...
متن کاملPlatonic polyhedra tune the 3 - sphere : Harmonic analysis on simplices
A spherical topological manifold of dimension n − 1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of reduction of group representations. A basis for the harmonic analysis on t...
متن کاملPlatonic polyhedra tune the 3 - sphere : Harmonic analysis on simplices . Peter Kramer
A spherical topological manifold of dimension n − 1 forms a prototile on its cover, the (n-1)-sphere. The tiling is generated by the fixpoint-free action of the group of deck transformations. By a general theorem, this group is isomorphic to the first homotopy group. Multiplicity and selection rules appear in the form of reduction of group representations. A basis for the harmonic analysis on t...
متن کاملDynamic Harmonic Modeling and Analysis of VSC-HVDC Systems
Harmonics have become an important issue in modern power systems. The widespread penetration of non-linear loads to emerging power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs a Dynamic Harmonic Domain (DHD) based framework for dynamic harmonic analysis of VSC-HVDC systems. These systems are wide...
متن کاملThe analysis of a Beam Made of Physical Nonlinear Material on Elastic Foundation Under a Harmonic Load
ABSTRACT: A prismatic beam made of a behaviorally nonlinear material situated on nonlinear elastic foundation is analyzed under a moving harmonic load moving with a known velocity. The vibration equation of motion is derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculat...
متن کاملTime Frequency Analysis of Higher Harmonic Generation in a Three Color Laser Pulse
high harmonic generation is a useful tool for the generation of short, intense attosecond pulses. In order to simulate high harmonic generation, we performed a numerical solution to the time dependent Schrödinger equation. by considering dipole approximation, we predicted generation of a 53 attosecond pulse. In order to see the time and frequency of emission of attosecond pulse, we exploit...
متن کامل