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The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the phase space usually consists of all possible values of the position and momentum parameters.
Remember that this change in velocity, ∆V, is only the amount required to change the spacecraft from its original orbit to the phasing orbit.A second change in velocity equal to the magnitude but opposite in direction of the first must be done after the spacecraft travels one phase orbit period to return the spacecraft from the phasing orbit to the original orbit.
Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature. Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is Maxwellian. This distribution function allows fluid ...
An event in the universe is caused by the set of events in its causal past. An event contributes to the occurrence of events in its causal future. Upon choosing a frame of reference, one can assign coordinates to the event: three spatial coordinates x → = ( x , y , z ) {\displaystyle {\vec {x}}=(x,y,z)} to describe the location and one time ...
At this point the phase space changes qualitatively and the dynamical system is said to have gone through a bifurcation. Bifurcation theory considers a structure in phase space (typically a fixed point, a periodic orbit, or an invariant torus) and studies its behavior as a function of the parameter μ. At the bifurcation point the structure may ...
In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations. The method consists of first rewriting the equations as a system of differential equations that are first-order in time, by introducing additional variables.
As the phase varies, the coherent state circles around the origin and the disk neither distorts nor spreads. This is the most similar a quantum state can be to a single point in phase space. Figure 5: Phase space plot of a coherent state. This shows that the uncertainty in a coherent state is equally distributed in all directions.
Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future. In physics , the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute ...