Start with a rotating rigid body, and compute its angular momentum. Rank0 tensors are called scalars while rank1 tensors are called vectors. Fisica i aula 9 rotacao, momento inercia e torque edisciplinas. The secondorder and higherorder tensors are symbolized with a boldface letter. 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. 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. Pick an origin and assume that the body is made up of n point masses m i at positions described by the vectors r i i 1. An ndimensional vector eld is described by a onetoone correspondence between nnumbers and a point. Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity.
The three basic types are called scalar product or inner product, cross product and outer product or tensor product. In generic terms, the rank of a tensor signi es the complexity of its structure. 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. Hence, the ith component of v relative to the basis e. By continuing to use this site, you consent to the use of cookies. 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. The stress at a point of an elastic solid is an example of a tensor which depends on two directions one normal to the area and other that of the force on it. How to calculate the moment of inertia section form of i example. Let us generalize these concepts by assigning nsquared numbers to a single point or ncubed numbers to a single. Introduction to tensor calculus a scalar eld describes a onetoone correspondence between a single scalar number and a point. 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. However, it is likely that teachers will wish to generate additional exercises.
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