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Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes.

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Summarizing from Murray, Li, and Sastry (chapters 3 and 5) there are 3 related things: Twist: An element of se(3) (which is a bit like the derivative of an element of SE(3), which is the set of tran …
answered Jul 18 '14 by ryan0270
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It is a mathematical concept call the "Special Euclidean" group. Roughly, it is a combination of a rotation and translation. You'll also frequently see SO3, which is the special orthogonal group which …
answered Sep 4 '17 by ryan0270
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Think of it this way, if you had 90$^\circ$ yaw you would swap roll and pitch, and maybe switch the sign depending on your coordinate system definition. Once you think through that, you just use the y …
answered Jan 27 '14 by ryan0270
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I think what you're missing is initial conditions; you need to define $\Omega$ at $t=0$. Give that angular velocity, you can then easily solve (4) for $\dot{R}$ and (5) for $\dot{\Omega}$. From that p …
answered Nov 16 '17 by ryan0270
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If everything were ideal, then your thinking is correct. In practice, though, there are many accumulated errors both in the sensors and in the real vs modelled Jacobian. So if what you care about most …
answered Jul 17 '19 by ryan0270
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In short answer: yes Kalman filter is a special case of an $H_2$ observer Yes Yes ... LQG is just Kalman filter + LQR controller, which are both special cases of $H_2$ Depends on use case. $H_2$ min …
answered Jul 11 '17 by ryan0270