Examples of tensor in the following topics:
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- All of these objects are examples of tensors.
- We can work out how tensors transform by looking at a few examples.
- The quantity is a tensor.
- We can find similar results for mixed tensors and covariant tensors.
- which defines the field tensor without reference to the potentials.
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- this is called the energy-momentum tensor or stress tensor of the system.
- The space-space part of the energy-momentum tensor must be symmetric, isotropic and a three-dimensional tensor (a matrix).
- The only tensor that works is
- Notice that the trace of the energy-momentum tensor $T^\mu_{~~\mu}$ is a scalar.
- Let's look at the non-relativistic limit of the energy-momentum tensor.
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- The other four muscles
are the tensor veli palatini, the mylohyoid,
the anterior belly of the digastric, and the tensor tympani.
- With the exception of the
tensor tympani, all of these muscles are involved in biting, chewing and
swallowing, and all have bilateral cortical representation.
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- For an ideal fluid we found that the stress tensor took a particular form,
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- Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.
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- This could be a scalar function or it could be a vector or even tensor function.
- Examples of tensor fields include the stress and strain inside continuous bodies.
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- The components of the stress-energy tensor must also be conserved
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- As we use mass, linear momentum, translational kinetic energy, and Newton's 2nd law to describe linear motion, we can describe a general rotational motion using corresponding scalar/vector/tensor quantities:
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- This tensor $\eta_{\mu\nu}$ defines the metric for flat spacetime.
- It is called the metric because you need it to convert various four vectors (and other objects tensors) into scalars that we can measure.