Parameters( )

Parameters(a, b, ...)

Notice that functionality has been attached to  automatically.

In a model where  is a constant, the above, with, is undesired. You would like to be able to define  in the simple way it has been done, and then have  return a result with , not . This situation is addressed by the Parameters command. For example:

In this way, instead of the undesired result , you now have the constant  defined as a parameter, with no functionality attached.

A typical use for the Parameters command is when computing equations of motion departing from a Lagrangian or a Hamiltonian (the Energy). Consider a harmonic oscillator of mass , and  is a constant parametrizing the restoring force. The Energy (Hamiltonian) in terms of the momentum  and position  is given by:

where in the above,  and  represent functions of time, while  and  represent constant parameters. Because  and  have been set by the Parameters command, no functionality is attached to them.

Now you can compute the Hamilton equations directly.

It is now easy to see that the Energy of this oscillator is a constant; that is, it does not depend on : differentiate the Energy (the Hamiltonian ), and introduce the equations of motion that were previously derived.

The same computation can be performed without using Parameters. Define  as a mapping, then you must use more complicated syntax to specify the parameters. See the last example in the help page for D for a demonstration of this method.

To query about the objects defined as parameters at any moment, enter the Parameters command with no arguments.

To unset the symbol  as a parameter, it suffices to unassign it.

Now  is not in the list of parameters, and it depends on  in the function .

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