Real hyperelliptic curve: Difference between revisions

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{{one source|date=February 2011}}
 
In [[applied mathematics]], a '''damping matrix''' is a matrix corresponding to any of certain systems of linear ordinary differential equations.
 
A '''damping [[Matrix (mathematics)|matrix]]''' is defined as follows. If the system has ''n'' [[Degrees of freedom (mechanics)|degrees of freedom]] ''u''<sub>''n''</sub> and is under application of ''m'' [[damping]] [[force]]s.
 
Each [[force]] can be expressed as follows:
 
: <math>f_{Di}=c_{i1} \dot{u_1}+c_{i2} \dot{u_2}+\cdots+c_{in} \dot{u_n}=\sum_{j=1}^n c_{i,j}\dot{u_j} \, </math>
 
It yields in [[Matrix (mathematics)|matrix]] form;
 
: <math>F_D=C \dot{U} \, </math>
 
where '''C is the [[damping]] matrix''' composed by the damping coefficients:
 
: <math>C=(c_{i,j})_{1\le i\le n,1\le j\le m} \, </math>
 
== References ==
 
*(fr) [http://www.enpc.fr/fr/formations/ecole_virt/cours/Pecker2009_2010/poly/Chapitre6.pdf Mechanics of structures and seisms]
 
[[Category:Mechanical engineering]]
[[Category:Classical mechanics]]
 
{{engineering-stub}}
{{physics-stub}}
{{mathapplied-stub}}

Revision as of 19:16, 11 September 2013

Template:One source

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

A damping matrix is defined as follows. If the system has n degrees of freedom un and is under application of m damping forces.

Each force can be expressed as follows:

It yields in matrix form;

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

References

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