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...mpact]], then the motion is said to be ''negatively Lagrange stable''. The motion through <math>x</math> is said to be ''Lagrange stable'' if it is both posi ...y-/negatively-/Lagrange stable if ''for each'' <math>x \in M </math>, the motion <math>\Phi(t,x)</math> is positively-/negatively-/Lagrange stable, respecti ...

== General Background<ref>Levine, W.S., “The Control Handbook”, CRC Press, 23 Feb 1996, Pg. 963.</ref> == == Flight Control Application == ...

{{Short description|Optimal control technique}} ...tness of Lagrangian systems underactuated by one control]” SIAM Journal on Control and Optimization, 36, 164,1998. </ref> ...

...dissipative in the sense that [[phase-space]] volume is not conserved. The motion is attracted to an equilibrium, in which the sleigh moves without rotation, ...he knife edge trails. Let ω be the angular velocity. Then the equations of motion are ...

...A Generalized Legendre–Clebsch Condition for the Singular Cases of Optimal Control |journal=IBM Journal of Research and Development |volume=11 |issue=4 |pages | title = Principles of Robot Motion: Theory, Algorithms, and Implementation ...

{{Short description|Robot control}} ...t1=Lynch |first1=Kevin M. |title=Modern robotics: mechanics, planning, and control |last2=Park |first2=Frank C. |date=2017 |publisher=Cambridge university pre ...

...MC)'''. In contrast with conventional [[sliding mode control]], the system motion under integral sliding mode has a dimension equal to that of the [[state sp ...ence/article/abs/pii/S0005109805000361 |title=Robust integral sliding mode control for uncertain stochastic systems with time-varying delay |journal=Automatic ...

...eudospectral Optimal Control: From Theory to Flight," ''Annual Reviews in Control,'' Vol.36, No.2, pp. 182–197, 2012.</ref> Nonsmooth Analysis and Control Theory, Springer–Verlag, New York, ...

...able thrust is limited, the transfer is occasionally posed as an [[optimal control]] problem subjected to the required objective and constraints. Relative motion in the orbit means the motion of a [[spacecraft]] orbiting a planet relative to the other spacecraft orbi ...

...beam's motion. The term is used primarily for [[electron]] beams, in which motion is often dominated by the space charge. ...d the generalized perveance <math>K</math><ref>Lawson, J. D., J. Electron. Control 5, 146 (1958).</ref><ref>M. Reiser, ''Theory and Design of charged particle ...

...motion proportional to the velocity. This may be affected by fluid flow or motion of magnetic structures. The intended effect is to improve the [[damping rat [[Category:Control theory]] ...

[[File:Aileron yaw.gif|thumb|right|200px|Yaw motion in an aircraft]] ...ges the direction it is pointing, to the left or right of its direction of motion. The '''yaw rate''' or '''yaw velocity''' of a car, aircraft, projectile or ...

...used in [[robotics]]|the equations used for describing [[Motion (physics)|motion]] in [[classical mechanics]]|Kinematics}} ...= Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators ...

...ublisher=Springer-Verlag|location=Berlin|date=2006|series=Lecture Notes in Control and Information Sciences|volume=334|isbn=978-3-540-32800-1}}</ref> Due to t The development of [[variable structure control]] depends upon methods of analyzing variable structure systems, which are s ...

{{Short description|Simplified model of orbital relative motion}} ...rcular orbit. This model gives a first-order approximation of the chaser's motion in a target-centered coordinate system. It is used to plan the rendezvous o ...

In [[kinematics]], the motion of a [[rigid body]] is defined as a continuous set of displacements. One-pa ...tial navigation in [[virtual reality]], computer-aided geometric design of motion via interactive interpolation, [[CNC]] [[tool path planning]], and task spe ...

Consider a pendulum. Because of how the motion of the weight is constrained by the arm, the velocity vector <math>\overrig In [[robot]] [[motion planning]], a '''Pfaffian constraint''' is a set of ''k'' [[linearly indepe ...

...rmined system]].<ref>{{Cite book|title=Dynamic Modeling of Musculoskeletal Motion - Springer|last=Yamaguchi|first=Gary Tad|publisher=|year=2001|isbn=978-0-38 ...metabolic cost).<ref>{{Cite book|title=Dynamic Modeling of Musculoskeletal Motion - Springer|last=Yamaguchi|first=Gary Tad|publisher=|year=2001|isbn=978-0-38 ...

...otational Inverted Pendulum: Classic pedagogical example of application of control theory]] ...Egeland, O. and Gravdahl, T. (2002) “Modeling and Simulation for Automatic Control”, Marine Cybernetics, Trondheim, Norway, 639 pp., {{ISBN|82-92356-00-2}}.</ ...

...physics)|dimension]]" ([[Rectilinear motion|rectilinear]] or [[Curvilinear motion|curvilinear]]), with [[unit (physics)|units]] of [[length]] (e.g., [[metre] {{Authority control}} ...