cartesian tensor造句

• Cartesian tensors achieve considerable computational simplification at the cost of generality and of some theoretical insight.
• Cartesian tensors are widely used in various branches of continuum mechanics, such as fluid mechanics and Cartesian-tensor indices are written as subscripts.
• Cartesian tensors are as in tensor algebra, but Euclidean structure of and restriction of the basis brings some simplifications compared to the general theory.
• For Cartesian tensors, only the order of the tensor matters in a Euclidean space with an orthonormal basis, and all indices can be lowered.
• Use of Cartesian tensors occurs in physics and engineering, such as with the Cauchy stress tensor and the moment of inertia tensor in rigid body dynamics.
• Cartesian tensors use tensor index notation, in which the variance may be glossed over and is often ignored, since the components remain unchanged by raising and lowering indices.
• In geometry and linear algebra, a "'Cartesian tensor "'uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components.
• While orthonormal bases may be found for some such coordinate systems ( e . g . tangent to spherical coordinates ), Cartesian tensors may provide considerable simplification for applications in which rotations of rectilinear coordinate axes suffice.
• The nine components " & sigma; ij " of the stress vectors are the components of a second-order Cartesian tensor called the " Cauchy stress tensor ", which completely defines the state of stress at a point and is given by
• There is a ( partially mnemonical ) correspondence between index positions attached to "'L "'and in the partial derivative : " i " at the top and " j " at the bottom, in each case, although for Cartesian tensors the indices can be lowered.
• Although Cartesian tensors do not occur in the theory of relativity; the tensor form of orbital angular momentum "'J "'enters the spacelike part of the relativistic angular momentum tensor, and the above tensor form of the magnetic field "'B "'enters the spacelike part of the electromagnetic tensor.