applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...

, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations. A damping

matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...

is defined as follows. If the system has ''n''

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

''u''_''n'' and is under application of ''m'' damping

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...

s. Each

can be expressed as follows: :

f_=c_ \dot+c_ \dot+\cdots+c_ \dot=\sum_^n c_\dot

It yields in

form; :

F_D=C \dot

where C is the damping matrix composed by the damping coefficients: :

C=(c_)_

References

*(fr
Mechanics of structures and seisms
Mechanical engineering Classical mechanics {{mathapplied-stub