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A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry. It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by an atom or group. [1] [2] [3] It can be represented generically as:
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
This 3-flat F represents space, and the homography constructed, restricted to F, is a screw displacement of space. Let a be half the angle of the desired turn about axis r, and br half the displacement on the screw axis. Then form z = exp((a + bε)r) and z* = exp((a − bε)r). Now the homography is
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
One example of a single displacement reaction is when magnesium replaces hydrogen in water to make solid magnesium hydroxide and hydrogen gas: + + Double displacement In a double displacement reaction , the anions and cations of two compounds switch places and form two entirely different compounds.
A neutralization reaction is a type of double replacement reaction. A neutralization reaction occurs when an acid reacts with an equal amount of a base. This reaction usually produces a salt. One example, hydrochloric acid reacts with disodium iron tetracarbonyl to produce the iron dihydride:
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. The distance between any two particles changes if and only if deformation has occurred. If displacement occurs without deformation, then it is a rigid-body displacement.
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