Maxwell’s eight equations as one quaternion equation

1978 ◽  
Vol 46 (4) ◽  
pp. 430-431 ◽  
Author(s):  
James D. Edmonds
Keyword(s):  
Quaternion Equation

scholarly journals Solution of a quadratic quaternion equation with mixed coefficients

2016 ◽  
Vol 74 ◽  
pp. 140-151 ◽  
Author(s):  
Rida T. Farouki ◽  
Graziano Gentili ◽  
Carlotta Giannelli ◽  
Alessandra Sestini ◽  
Caterina Stoppato
Keyword(s):  
Quaternion Equation

scholarly journals Dependence of the amplitude of transverse oscillations of the axisymmetric UAV rotating around the longitudinal axis on the residual imbalance

2020 ◽  
pp. 80-87
Author(s):  
Kostyantyn Ponomorenko ◽  
Dmytro Gorbachek
Keyword(s):  
Rotation Velocity ◽  
Longitudinal Axis ◽  
Explicit Dependence ◽  
Arithmetic Average ◽  
Amplitude Increase ◽  
Quaternion Equation ◽  
Aerodynamic Asymmetry ◽  
Orientation Quaternion ◽  
The Relationship ◽  
Transverse Oscillations

The analysis of the relationship between residual imbalance of an axisymmetric cylindrical UAV, and the amplitude of its prevailing transverse oscillations during the flight. The residual imbalance of an UAV that rotates along the roll and its effect on the amplitude of the vehicle`s transverse oscillations in real flight are discussed and investigated. The total imbalance and the average imbalance of UAV were calculated on the basis of dynamic imbalance measurements in two planes. Flight data from twelve UAV launches was obtained for this dependence analysis. During angular velocity sensors signals processing an orientation algorithm with one quaternion equation was applied. Eiler-Krylov angles were obtained from the resulting orientation quaternion and an average and total imbalance influence on transverse oscillations amplitude was investigated. During the analysis of the tests held, it is possible to make a conclusion that transverse oscillations amplitude directly depends on the magnitude of residual imbalance. Transverse oscillations amplitude mostly depends on average imbalance (which is arithmetic average between imbalance magnitudes in every plane of measurement) and it depends less on total imbalance (which is geometric sum of imbalance vectors in every plane of measurement): average imbalance change from 100 g∙mm to 700 g∙mm caused transverse oscillations amplitude change from 0,5° to 2°. In some cases we will see spread of oscillations amplitude values up to ±1° relatively approximation line, this is due to other factors influence, besides imbalance, such as aerodynamic asymmetry. However, the tendency of oscillations amplitude increase with the increase of imbalance is preserved. The obtained results give us an explicit dependence of transverse oscillations amplitude of UAV from its dynamic imbalance in specific conditions of flight (velocity, type of trajectory and rotation velocity) and with specific UAV parameters (aerodynamic, mass-inertial and other parameters). Change of these parameters may cause change of specific quantitative parameters of obtained dependence, but its nature remains the same. The mass of the investigated UAV was approximately 15 kg, trajectory was ballistic, flight speed was transonic and subsonic, rotation velocity around longitudinal axis was 1..7 rounds per second.

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