Gyroscopes & The Earth

The Gyroscope

The Gyroscope

The Gyroscope : http://youtu.be/cquvA_IpEsA

Ever wondered how a Gyroscope acts in space

Ever wondered how a Gyroscope acts in space : http://youtu.be/kCyMZFwb_O8, it just sits there!

When a gyroscope in space is poked : http://youtu.be/kCyMZFwb_O8, it might wobble, but will not spin.
When a gyroscope in space is poked : http://youtu.be/kCyMZFwb_O8, it will move backwards without spinning.

Oscillating Gyroscopes are complex to describe in maths, but fun to watch

Oscillating Gyroscopes are complex to describe in maths, but fun to watch (Nutation) : http://youtu.be/5Sn2J1Vn4zU

How does a gyroscope work?

The gyroscope & conservation of momentum

The gyroscope & conservation of momentum : http://youtu.be/3a7QXBu_rEM

Conservation of Angular Momentum (with a bicycle gyro-wheel)

Conservation of Angular Momentum (with a bicycle gyro-wheel) : http://youtu.be/UZlW1a63KZs

(double) Gyroscopes and a thing called precession

(double) Gyroscopes and a thing called precession : http://youtu.be/vGun5athdfg

A balanced gyroscope, resisting a constant-mass by rotating

A balanced gyroscope, resisting a constant-mass by rotating : http://youtu.be/3BN1a6IVocQ

Gyroscope precession when plane tail suddenly lifts off from runway

Gyroscope precession when plane tail suddenly lifts off from runway : http://youtu.be/T0vs2AMJDas

Gyroscopes, atomic nuclei, precession & resonance to natural frequencies of precession (T)

Gyroscopes, atomic nuclei, precession & resonance to natural frequencies of precession (T) : http://youtu.be/7aRKAXD4dAg

The Cubli

The Cubli, it can walk, balance, jump, & build stuff : http://youtu.be/bGskTx0P7MI #gyroscopes

Ice ages on Earth (orbital variables)

Year On Earth and how it relates to Ice Ages (rotation & orbital variables) : http://youtu.be/IhqzW97_47w

reference [wiki]: http://en.wikipedia.org/wiki/Semi-major_axis

The Earth Year

The elliptical orbit of the earth does change shape, becoming more elliptical, and more circular. The Semi-major axis length of the ellipse does not change, so a sidereal year (a year measured by the star’s position) does not change.

The Precession of the Earth

Earths tilt can vary between 22.1 degrees to 24.5 degrees. It is currently at a axial tilt of 23.4 degrees and is declining. This change in tilt angle change has a cycle of 41,000 years. This change in tilt is directly related to Ice Ages on earth. Of course the 100,000 year cycle of the elliptical orbit of the earth wobbling, or moving up and down on the invariable plane (roughly the orbit of Jupiter) also is directly related to the Ice Ages (there is more about this below).

This would indicate that two waveforms (in global earth temperatures) in time are influencing the Ice Ages because of the way the earth spins and orbits the sun. Ice Ages (global temperatures) may also be influenced by other factors such as green house gases for example, and even the fact that life exists on the earth.

Mars has a more extreme variation in the change of its rotational axis tilt

Because Mars has only got two very small moons, those moons don’t affect the tilt of Mars (reduce its change over time), and so the tilt of Mars is primarily a function of the Suns influence. Because of this Mars’ axis can tilt anywhere from 15° to 35°. This tilt variation will be a factor in determining when Ice Ages occur on Mars.

While the stretching of the elliptical orbit of the Earth does not seem to be a major factor in the Ice Ages, possibly because of additional requirements like high tilts make seasonal variations more harsh and add to the problem. The stretching of Mars’ orbit into more elliptical form does seem to influence Ice Ages. The stretching of Mars’ elliptical orbit has a cycle of 51,000 years and is in step with the axial tilt variation (mentioned below here for Mars).

The axial tilt variation of Mars has a cycle of 2.5 million years, this is a much larger time scale when compared to Earth’s 41,000 years.

Mars’ pole precession has a cycle of 51,000 years (the Earths precession is 26,000 years).

Reference

THE PRECESSION OF THE EARTH CONTINUED

It takes the earth around 26,000 years to precess through one cycle, the earths axis traces out a circle in the (sky) star map (or 3D cone shape in real 3D space). during precession, the axis of the earth traces out a circle in the sky (at a extremely slow rate). This means that the identity of the North Star changes very slowly over time. In 14,000 years Vega will be the North Star (pole star).

The severity of seasons, is effected by this precession, right now the southern side of the earth has more sever changes in temperature when the changes from one season to another is considered, while the northern part of the world has less severe changes in temperatures as the seasons change.

seasons

The above diagram illustrates how the norther part of earth (side b) has milder changes in the seasonal temperatures, while the southern side of earth (side a) has more severe temperature changes as the seasons change.

The axial tilt of the earth is a function of the forces applied primarily by the sun and the moon.

The Precession of Earth : http://youtu.be/0qHjtp4cdCA

earthorbit

The earths orbit (an ellipse) is also rotating around the sun, as the above trace of earth’s elliptical orbit (in yellow) shows. further, the orbit itself changes from a more elliptical shape to a more circular shape (but the time of a year still remains the same in such cases). This movement of the “ellipse” causes the sun to move through the constellations of the zodiac, when you view them at the same time every year over a very long time span.

To prevent this constant spiral pattern from being a problem, we measure a year based on the positions of the stars. This is called a sidereal year.

The spinning of the ellipse (earths orbit) is caused by the interaction of the earth with other planets. It takes about 112,000 years for a complete orbit of the ellipse (relative to fixed stars). This is considered to be a form of precession.

Both the earths axis and earth’s elliptical orbit are in precession, and this effect adds, and results in it taking the Earth’s axis 21,000 years to go from one aphelion to another aphelion in the as the Earth’s elliptical orbit changes (the whole elliptical pattern rotating around the sun). Because of this, the aphelion and perihelion advance and average of 1 day every 58 years (this must be a time adjustment to when the seasons–summer and winter–will occur).

Jupiter and Saturn (but other planers do play a very small part) create a force on the Earth that changes how elliptical the Earth’s orbit is (or how close to a circle the Earth’s orbit is). This cycle of stretching and contacting the elliptical orbit takes around 100,000 years.  This means winters on the far side of the orbit can be considerably longer when the Earth’s orbit is at its maximum elliptical shape.

EARTH’S ELLIPTICAL ORBIT ALSO DRIFTS UP AND DOWN RELATIVE TO THE REFERENCE ORBITAL PLANE (WHICH ROUGHLY CORRESPONDS TO THE ORBIT OF SATURN)

ellipsewobble

The Earth’s elliptical orbit also wobbles up and down has a cycle of around 100,000 years around the invariable plane (http://en.wikipedia.org/wiki/Invariable_plane) which is roughly the orbital plane of Jupiter. The up and down motions of the Earth’s elliptical orbit can also be measured relative to the stars and it then has a cycle of 70,000 years.

The 100,000 year cycles also closely matches the pattern of the Ice Ages.

Gyroscope-Nutation

This section is a little technical, so please skip this section if you are not into the really strange and complex part of maths. Hope to find a reference for you that explains this in a easy to understand way.

A lot of complex maths is often used to describe things that might be easy to explain in example driven video, so don’t let anyone tell you it is too complex to explain, because it is quite possible that they are not good at communicating or that they are still not confident about the connection between the maths and the real world—converting generalized maths that could apply to several things into specific examples is not always easy.

This stuff is quite difficult to understand, because of the maths that is involved. If you come from another field such as electronics, you might be more comfortable with modeling the gyroscope using electronics, so a reference link to that kind of maths is provided here also.

Gyroscope-Nutation : http://youtu.be/5Sn2J1Vn4zU

Reference: http://funphysicsfacts.dyndns-wiki.com/groups/fun_physics_facts/revisions/25668/9/

Have a feeling this will also be able to be modeled in a electronic way, so this reference is also included: http://funphysicsfacts.dyndns-wiki.com/groups/fun_physics_facts/wiki/929f7/Electronics__Laplace_Transforms_Electronics_Applications.html & general ref: http://funphysicsfacts.dyndns-wiki.com/groups/fun_physics_facts/

The modeling aspect for people who like electronic equations is referenced here:

 The Water Analogy to Electricity

This section is rally just an advance on Analogous Electrical and Mechanical Systems, and shows that it can be applied to fluids.

Students are often given analogies of how electricity resembles water. There is criticism of this technique of teaching might end up confusing people more then helping them.

People that have studied fluids or electrical circuits, and especially control system (uses very complex maths) might find it comforting to use familiar maths equations of their fields, so such an analogy might be interesting and useful in such cases, to make sure the equations are being used and “developed/derived” correctly.

Chargingcct

This circuit can resemble another system, for example the filling of two water tanks. In the case of the water tanks, with the pump in pipe attached to the bottom of the water tanks: they are filling up with water, and that water pressure eventually negates the pressure of the pump and the flow of water eventually stops. In the case of the capacitors they are filling up with electrical charge. Both systems then have stored energy. To release the energy from the electrical circuit, we could short circuit the capacitors, or we could take out the voltage source, and replace it by a short circuit (a wire).

To release the water we would just block the pump pipe, possibly by closing a tap, and opening a tap that let to the water being released onto the ground.

Modeling is a tricky business, as the model may not apply to all situations. As we have seen above, the way the pipes are attached to the water tank does matter, if we attached the pipes to the top of the water tanks, then this model world not apply as now there is no back pressure when the tank fills up. Also in practice, inlet pipes from the pump side would be built in the top of the tank, and one or more sensors would tell the pump when to stop (such as floatation devices).

For the water case resistance might model the resistance of a pipe to the flow of water, and the high of the water in the tanks might resemble voltage, and finally the flow rate of the water might resemble current.

The only thing left to do now would be to produce the maths equations, and see if this is true for this particular case.

System Dynamics Tutorial 6

This is a video that describes how basic analogies, but does not go into examples of how such analogies might be used in a complex system or system with several components. If you are used to writing down equations for systems, then this task should be easier, as you simply swap over to a mechanical or electrical system’s equation using the analogies you have learned. Some hint is also used to give you more generalized modeling such as checking out how transformers might be used to model gears.

System Dynamics Tutorial 6 – Fundamental Analogies between Mechanical and Electrical Systems : http://youtu.be/Sf8X501RTgg

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Last edited in May 2014

Shortened link to article: Gyroscopes and The Earth [article]: http://wp.me/p10Tww-2T9

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