The astronomical model of precession asumes that the current movement of the vernal point is a constant motion.

This model guides to a period of 25771 years until the vernal point returns to its initial point. But this number can
be wrong if the motion of the vernal point has long term fluctuations.
Such an effect may be caused by unknown galatical phenomenons or fluctuations in gravitational fields.

Sri Yukteswar's View

Sri Yukteswar exposes his view about the yugas and the movement of the vernal point in the first chapter of his
illustrious book The Holy Science (Kalyana Darshanam).

According to the Holy Science the period for the movement of the vernal point is 24,000 years.

Sri Yukteswarji combines the movement of the vernal point with the theory of the Yugas.
According to his view Kali Yuga's duration is 2400 years (ascending and descending each 1200),
and the start of ascending Kali Yuga begins when the vernal point is 0 Aries.
Dwapara Yuga follows and has double duration, each Treta Yuga has 3600 years and each Satya Yuga 4800 years.

Therefore we have the sequence of Yugas shown in the table below.

Yuga

Duration (Years)

Vernal Point (Start)

Vernal Point (End)

Kali (ascending)

1200

00 Aries

12 Pisces

Dwapara (ascending)

2400

12 Pisces

06 Aquarius

Treta (ascending)

3600

06 Aquarius

18 Scorpio

Satya (ascending)

4800

18 Scorpio

00 Libra

Satya (descending)

4800

00 Libra

18 Cancer

Treta (descending)

3600

18 Cancer

24 Taurus

Dwapara (descending)

2400

24 Taurus

18 Aries

Kali (descending)

1200

18 Aries

00 Aries

Total

24,000

Emulating Sri Yukteswar's Ayanamsa

This ayanamsa can be emulated with several methods.

1. Using the Ayanamsa with the astronomical period

First method of emulation is to take a fixed start date with known Ayanamsa and use the astronomical period.
This is what the Sri Yukteswar Ayanamsa of swiss ephemeris does.

Disadvantage of this method is that long term predictions are not correct because the period is wrong.

2. Define a Custom Period

Second method is to take (again) a fixed start date with known Ayanamsa, but to use the period of 24,000 years given
by Sri Yukteswar. This kind of calculation can be configured in Maitreya.

Disadvantage of the method is that the actual true movement of the vernal point is neglected.

3. Define a Movement that Satifies Astronomical Precession and the Given Period

This method is a mix of the above methods. It assumes that the current precession is correct but has sigificant fluctuations
that lead to a total period of 24,000 years.

The current precession is too slow to get a period of 24,000 years. So it must be near a minimum. The speed must grow
in later periods to get the desired total period.

Possible positions for the minimum could be the point 0 Aries or the point in opposite to the supergalactic center
(i.e. around 26 Pisces).

Concluding Thaughts

It is possible to give mathematical equations for the 3rd method. A simple eliptic equation could be satisfiying for the
first time.

Investigations regarding long term Ayanamsa can be made taking old sources that rely on chitra paksha (i.e. Lahiri)
ayanamsa.
Most contemporary authors do not rely on old sources and pretend that they are not correctly calculated.