Mathematics Homework Solutions

Show equivalence of two versions of angular momentum equations by vector math.

I need to show that the following two terms are equivalent: l = m(r2I – rr)∙ω l = r x mv = r x m(ω x r) where r is the position vector from the origin to the particle l is the angular momentum I is the identity tensor ω is the vector angular velocity x indicates a cross product rr is a dya ...continues

Force and Opposing Force : Find maximum speed attained and distance travelled.

A particle of mass 10kg, moving in a straight line, starts at rest from a point A under the action of a force that decreases uniformly from 20N to zero in 20 secs. It then travels with a constant speed for a further 20s, and finally moves under the action of an opposing force of 40N until it comes to rest at B. Find the maximum ...continues

Vector Spaces : Simplifying Expressions and Index Notation

Please see the attached file for the fully formatted problems.

Vector Spaces : Direct Tensor Notation

Please see the attached file for the fully formatted problems.

Dyads and Tensor Vector Transformations

Please see the attached file for the fully formatted problems.

Tensors, Basis and Volume Orientation Function

Please see the attached file for problems: A - C.

Tensors, Eigenvectors, Eigenvalues and Polar Decomposition

Please see the attached file for problems: D - G.

Tensors and Maximization

Please see the attached file for the fully formatted problems.

Continuum Mechanics : Tensor Components and Basis

Please see the attached file for the fully formatted problems.

Browse