[SciPy-User] Understanding parameters of scipy.special Mathieu_cem function etc.

[Austin Tobin]

Mark,
Corrected link  wikipedia Mathieu_function
<https://en.wikipedia.org/wiki/Mathieu_function>
Unfortunately I do not know exactly what I am looking for.
I am trying to achieve something like what was done in this paper
<https://www.researchgate.net/profile/S_Taylor3/publication/3358134_Simulation_of_ion_trajectories_through_the_mass_filter_of_a_quadrupole_mass_spectrometer/links/00b4953bc5f0e9dfaf000000/Simulation-of-ion-trajectories-through-the-mass-filter-of-a-quadrupole-mass-spectrometer.pdf>.
At least starting with getting the trajectories.

Warren,
I have found that "a" is the characteristic number and "q" is the
characteristic parameter.

While it makes perfect sense that the function is periodic over a certain
range of values.
I will have to go further to apply this function to my problem, maybe I
just don't have the mathematics to make the connections.


Regards,
Austin Tobin

On Wed, Jul 26, 2017 at 8:36 PM, Warren Weckesser <
warren.weckesser at gmail.com> wrote:

>
>
> On Wed, Jul 26, 2017 at 5:52 AM, Austin Tobin <austin.tobin at gmail.com>
> wrote:
>
>> I am trying to relate the Mathieu equation found in Wikipedia Mathieu
>> Equation <https://en.wikipedia.org/wiki/Mathieu_function/> to the one
>> implemented in scipy.special. In Wikipedia there are 3 inputs, a,q and the
>> parameter along which the integration proceeds.
>>
>> mathieu_cem takes three inputs, an order (integer), a characteristic
>> parameter and the the parameter along which the integration proceeds in
>> degrees. I am trying to relate a and q to the order and characteristic
>> parameter.
>>
>
> In the Mathieu equation, 'a' is an arbitrary parameter.  However, for a
> given 'q', there is only a discrete set of values of 'a' for which the
> equation has even periodic solutions.  Call these a_0(q), a_1(q), a_2(q),
> etc.  'mathieu_a(m, q)' computes a_m(q), and 'mathieu_cem(m, q, x)' is the
> even periodic solution associated with a_m(q).
>
> Warren
>
>
> If it helps I am trying to simulate a quadrupole mass spectrometer with a
>> and q being trapping parameters.
>> Regards,
>> Austin
>>
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