Let us generalize these concepts by assigning nsquared numbers to a single point or ncubed numbers to a single. From this construction, if v vie i is a vector in v, then by taking the inner product with ei we have ei v ei vje j v j. Tensor is a tool written in ruby that helps provide an estimate on the cost of change on test source code based on a radical change in design on production source code, especially around branch execution code. Fisica i aula 9 rotacao, momento inercia e torque edisciplinas. Hence, the ith component of v relative to the basis e. Several times during the preparation of this book we taught a one semester course to students with a very limited background in linear algebra and no background in tensor analysis. The three basic types are called scalar product or inner product, cross product and outer product or tensor product. An ndimensional vector eld is described by a onetoone correspondence between nnumbers and a point. Quantities that have magnitude and two directions, e. In rowvector notation, the basis vectors themselves are just i ex 1,0,0 j ey 0,1,0 k ez 0,0,1 1. Introduction to tensor calculus a scalar eld describes a onetoone correspondence between a single scalar number and a point. The secondorder and higherorder tensors are symbolized with a boldface letter.
Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity. The firstorder tensor is symbolized with a boldface letter and by an arrow at the top part of the vector, i. Elementary tensor analysis this appendix is intended to provide the mathematical preliminaries needed for a clear and rigorous presentation of the basic principles in continuum mechanics. However, it is likely that teachers will wish to generate additional exercises. The reader is expected to be familiar with some notions of vector spaces or matrix algebra. Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of. Start with a rotating rigid body, and compute its angular momentum. Rank0 tensors are called scalars while rank1 tensors are called vectors. How to calculate the moment of inertia section form of i example.