Class DYAD

• Defined in theory: Tensor-quantities
• Source code: tensor-quantities.lisp

Slots on this class:

Documentation:

The class of second order tensors (aka tensors). Given an orthornormal basis a dyad can be decomposed into scalar components. These components can be represented as a square matrix. The matrix is not unique but it a 'view' of the tensor for a particular basis.

Subclass-Of: Constant-quantity, Tensor-quantity

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Slots on instances of this class:

Tensor-Order: 2

Axioms:

(<=> (Dyad ?D)
     (And (Constant-Quantity ?D)
          (Tensor-Quantity ?D)
          (= (Tensor-Order ?D) 2)
          (Forall (?B ?I ?J)
                  (=> (And (Orthonormal-Basis ?B)
                           (= (Basis.Dimension ?B)
                              (Spatial.Dimension ?D))
                           (Positive-Integer ?I)
                           (=< ?I (Spatial.Dimension ?D))
                           (Positive-Integer ?J)
                           (=< ?J (Spatial.Dimension ?D)))
                      (And (Defined (Dyad-Component ?D ?I ?J ?B))
                           (= (Quantity.Dimension (Dyad-Component ?D
                                                                  ?I
                                                                  ?J
                                                                  ?B))
                              (Quantity.Dimension ?D)))))
          (Forall (?U)
                  (=> (And (Unit-Of-Measure ?U)
                           (= (Quantity.Dimension ?U)
                              (Quantity.Dimension ?D)))
                      (Numeric-Tensor (Magnitude ?D ?U))))))