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Furthermore the unstable direction is symmetric. .
Furthermore the unstable direction is antisymmentric.
Furthermore the unstable direction is symmetric.
For instance, if the transverse displacement was 0.3 mm, the loss in the output power was 9.6% and a sidelobe appeared in the unstable direction.
Such solutions have only one unstable direction; the corresponding unstable manifold consists of two heteroclinic connections to the stable solutions (green and red dots).
If the equivalent velocity error in the unstable direction becomes too large, the orbit can become unrecoverable, leading to a departure from the environment of the Lagrange point within a few months.
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Hence we allow both the stable and unstable directions to be infinite dimensional.
Our approach is of purely dynamical systems, which depends on a detailed analysis of asymptotic stable and unstable directions.
It follows that for ( s > 0 ), ( mathcal {P}_E ( s ) ) measures the fight between complexity and dispersion in the unstable directions.
The constructive solution is independent of the controller dynamics so that the size of the (necessarily bounded) operating region in the exponentially unstable directions of the plant state space is large.
Then, the noise on the element Sk is propagated along the vibrational mode associated with the one unstable transversal direction, whose conditional exponent is λ2.
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