Introduction to the Variational Formulation in Mechanics

1Vector and Tensor Algebra

1.1 Points and Vectors

Consider the three‐dimensional Euclidean space, denoted by , whose geometry is built upon a set of primitive elements called points. Note that is not a vector space in the sense of the algebra because the addition of points is a concept without meaning.

The difference between two points and of space is defined by

(1.1)

where is the vector whose origin is in and ends at . All the vectors which can be determined through the differences between points belonging to form the set associated with . The set is a (real) vector space, where the ...