1978
DOI: 10.1016/0346-251x(78)90019-2
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Cited by 6 publications
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“…In that case, the conclusions of this section would not be applicable. Nevertheless, there are orbits, such as polar ones, in which the magnetic field rotates enough to ensure that dissipation along the orbit will occur in all directions [25].…”
Section: Mathematical Analysis Of the Law Under Stable Conditionsmentioning
confidence: 99%
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“…In that case, the conclusions of this section would not be applicable. Nevertheless, there are orbits, such as polar ones, in which the magnetic field rotates enough to ensure that dissipation along the orbit will occur in all directions [25].…”
Section: Mathematical Analysis Of the Law Under Stable Conditionsmentioning
confidence: 99%
“…The dependence on the variable can be eliminated with the following change of variable: (23) Resulting in the following set of equations: (24) The equilibrium attitude will occur only for certain values of angle θ. Therefore, a fourth equation that describes its variation may be used in the space state: (25) with ( 22) and ( 25) the following space state matrix for the variable Q can be constructed: (26) This state space system has an equilibrium point at: (27) This equilibrium point corresponds to a solution where the magnetic moment only produces torque about the y body axis, and the angular velocity increases until the spinning torques (that are independent of spin velocity) and despinning torques (that are proportional to spin velocity) compensate each other. Linearizing around that point: (28) where can be considered almost constant near the equilibrium point, because if θ, ω x and ω z are close to zero, therefore also (see equation ( 14)).…”
Section: Mathematical Analysis Of the Law Under Stable Conditionsmentioning
confidence: 99%