For a rigid object, the mass moment of inertia matrix is given by [1] = |lyx Iyy Iyz [Ix Iy Iz] where Iy = Iyx Iyz = Izy Ixz = Ix. Hence, [I] is a symmetric matrix. Here Ir denotes the mass moment of inertia around the X-axis when the objects are rotated around the x-axis, Iry denotes the mass moment of inertia around the y-axis when the objects are rotated around the x-axis, and so on. Eigenvalues of the inetria matrix are the principle mass moments of inertia; I1, l2, and I3; and the eigenvectors of the inertia matrix form the directions of the principle axes of the rigid body according to which of the principal mass moments of inertia (I1,12,13) are defined. Consider the given inertial matrix for a rigid body in motion: 52 0 441 I = 50 25 kg m2. | 44 25 60 Find the principal moments of inertia and the directions of principle axes of the rigid body.
For a rigid object, the mass moment of inertia matrix is given by [1] = |lyx Iyy Iyz [Ix Iy Iz] where Iy = Iyx Iyz = Izy Ixz = Ix. Hence, [I] is a symmetric matrix. Here Ir denotes the mass moment of inertia around the X-axis when the objects are rotated around the x-axis, Iry denotes the mass moment of inertia around the y-axis when the objects are rotated around the x-axis, and so on. Eigenvalues of the inetria matrix are the principle mass moments of inertia; I1, l2, and I3; and the eigenvectors of the inertia matrix form the directions of the principle axes of the rigid body according to which of the principal mass moments of inertia (I1,12,13) are defined. Consider the given inertial matrix for a rigid body in motion: 52 0 441 I = 50 25 kg m2. | 44 25 60 Find the principal moments of inertia and the directions of principle axes of the rigid body.
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![For a rigid object, the mass moment of inertia matrix is given by
[Ix Iy Iz
1 = Iyx lyy lyz
[Ix Iy Iz
where
Iy = lyx
Iyz = Izy
Ixz = Ix.
Hence, [I] is a symmetric matrix. Here I denotes the mass moment of inertia around the
X-axis when the objects are rotated around the x-axis, Iry denotes the mass moment of inertia
around the y-axis when the objects are rotated around the x-axis, and so on. Eigenvalues of
the inetria matrix are the principle mass moments of inertia; I1, I2, and I3; and the eigenvectors
of the inertia matrix form the directions of the principle axes of the rigid body according to
which of the principal mass moments of inertia (I1,12,13) are defined.
Consider the given inertial matrix for a rigid body in motion:
Г52
44
I =
50 25 kg m2.
44 25 60
Find the principal moments of inertia and the directions of principle axes of the rigid body.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37eec9f2-4e89-4eee-8340-c70983047879%2Fe12ee045-d794-4f34-beab-d797404361b6%2Fi0s16ko_processed.png&w=3840&q=75)
Transcribed Image Text:For a rigid object, the mass moment of inertia matrix is given by
[Ix Iy Iz
1 = Iyx lyy lyz
[Ix Iy Iz
where
Iy = lyx
Iyz = Izy
Ixz = Ix.
Hence, [I] is a symmetric matrix. Here I denotes the mass moment of inertia around the
X-axis when the objects are rotated around the x-axis, Iry denotes the mass moment of inertia
around the y-axis when the objects are rotated around the x-axis, and so on. Eigenvalues of
the inetria matrix are the principle mass moments of inertia; I1, I2, and I3; and the eigenvectors
of the inertia matrix form the directions of the principle axes of the rigid body according to
which of the principal mass moments of inertia (I1,12,13) are defined.
Consider the given inertial matrix for a rigid body in motion:
Г52
44
I =
50 25 kg m2.
44 25 60
Find the principal moments of inertia and the directions of principle axes of the rigid body.
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