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
˙
+
⋯
+
c
i
n
u
n
˙
=
∑
j
=
1
n
c
i
,
j
u
j
˙
{\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
=
(
c
i
,
j
)
1
≤
i
≤
n
,
1
≤
j
≤
m
{\displaystyle C=(c_{i,j})_{1\leq i\leq n,1\leq j\leq m}}
