2.7 KiB
2.7 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Damping matrix | 1/1 | https://en.wikipedia.org/wiki/Damping_matrix | reference | science, encyclopedia | 2026-05-05T11:46:56.497350+00:00 | kb-cron |
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:
f
D
i
=
c
i
1
u
1
˙
+
c
i
2
u
2
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+
⋯
+
c
i
n
u
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∑
j
=
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n
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,
j
u
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{\displaystyle 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}}}}
It yields in matrix form;
F
D
=
C
U
˙
{\displaystyle F_{D}=C{\dot {U}}}
where C is the damping matrix composed by the damping coefficients:
C
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(
c
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,
j
)
1
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m
{\displaystyle C=(c_{i,j})_{1\leq i\leq n,1\leq j\leq m}}