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* In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. [ 2 ] More generally in conservative systems , equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero.
They make it possible to approximately separate rotation from vibration. Although the rotational and vibrational motions of the nuclei in a molecule cannot be fully separated, the Eckart conditions minimize the coupling close to a reference (usually equilibrium) configuration. The Eckart conditions are explained by Louck and Galbraith. [2]
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body.
The boundary condition is the no slip condition. This problem is easily solved for the flow field: u ( y ) = y − y 2 2 . {\displaystyle u(y)={\frac {y-y^{2}}{2}}.} From this point onward, more quantities of interest can be easily obtained, such as viscous drag force or net flow rate.
[23]: 58 When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium. A state of mechanical equilibrium is stable if, when the position of the body is changed slightly, the body remains near that equilibrium. Otherwise, the equilibrium is unstable.
The static equilibrium of a mechanical system rigid bodies is defined by the condition that the virtual work of the applied forces is zero for any virtual displacement of the system. This is known as the principle of virtual work. [5] This is equivalent to the requirement that the generalized forces for any virtual displacement are zero, that ...
The Gibbs rotational ensemble represents the possible states of a mechanical system in thermal and rotational equilibrium at temperature and angular velocity. [1] The Jaynes procedure can be used to obtain this ensemble. [2] An ensemble is the set of microstates corresponding to a given macrostate.