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Consequently, the object is in a state of static mechanical equilibrium. In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. [1]: 39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. [1]: 45–46 [2]
The static equilibrium of a particle is an important concept in statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three directions are equal ...
In other words, the configuration of particle A in state 1 and particle B in state 2 is different from the case in which particle B is in state 1 and particle A is in state 2. This assumption leads to the proper (Boltzmann) statistics of particles in the energy states, but yields non-physical results for the entropy, as embodied in the Gibbs ...
Typically, a human's center of mass is detected with one of two methods: the reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that ...
A classical particle under the influence of a force accelerates according to Newton's second law, a = m −1 F, or alternatively, the momentum changes according to d / dt p = F. This intuitive principle appears identically in semiclassical approximations derived from band structure when interband transitions can be ignored for ...
The non-equilibrium flow is superimposed on a Maxwell-Boltzmann equilibrium distribution of molecular motions. Inside a dilute gas in a Couette flow setup, let u 0 {\displaystyle u_{0}} be the forward velocity of the gas at a horizontal flat layer (labeled as y = 0 {\displaystyle y=0} ); u 0 {\displaystyle u_{0}} is along the horizontal direction.
In computational mechanics, Guyan reduction, [1] also known as static condensation, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial terms of the equilibrium equations and expressing the unloaded degrees of freedom in terms of the loaded degrees of freedom.
Since every particle needs to be in equilibrium, this reaction stress will generally propagate from particle to particle, creating a stress distribution throughout the body. The typical problem in stress analysis is to determine these internal stresses, given the external forces that are acting on the system.