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

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

Austin Tobin

I am trying to relate the Mathieu equation found in Wikipedia Mathieu Equation 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.

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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Re: Understanding parameters of scipy.special Mathieu_cem function etc.

Warren Weckesser-2


On Wed, Jul 26, 2017 at 5:52 AM, Austin Tobin <[hidden email]> wrote:

I am trying to relate the Mathieu equation found in Wikipedia Mathieu Equation 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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Re: Understanding parameters of scipy.special Mathieu_cem function etc.

Austin Tobin
Mark,
Corrected link  wikipedia 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. 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 <[hidden email]> wrote:


On Wed, Jul 26, 2017 at 5:52 AM, Austin Tobin <[hidden email]> wrote:

I am trying to relate the Mathieu equation found in Wikipedia Mathieu Equation 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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