studiot

One of the things about quoting Einstein is that he often wrote several versions of his papers as time went on. For instance compare the 1920s, 30 40s and 50s versions of sundry papers about Space, Time, Ether, and Geometry.

I think the late Victorians have already done this. However it is difficult to say since the electrical parameters have not been fully specified. I can say the no 'Faraday Electromotive Force' will be created however. Ned, can you say what electric field strength you expect between the plates and explain why you need a current controller ?

Well I am not convinced. From Archimedes to Romer to Cavendish to Thompson to Einstein to Buckminster Fuller, the difference between scientists who successfully introduced their ideas and hand waving theorists like Plato is that they all said words to the effect "Here is a real physical object. I have an idea that predicts that if I kick it in a certain way it will respond according to my idea" The thing is they were all also practical men who were also able to state the practical 'certain way'.

Click somewhere on my name/ avatar. At the top on the details about me, next to my name you will se two blue boxes. The first says follow member The second says message. click on that and send your message. Not even the mods can read it without invitation.

No I mean this forum's private messaging system. I have done this before. There will be too many to post on that system directly. I do not want your private e-mail, I suggest something like gmail as I know they can recieve the file sizes I generate. There will be no colour since the book is entirely B&W, with file sizes in the 250k - 500k range probalbly. Also I can split over more than one email. Just be aware that many email systems will put unknown senders straight into the spam box.

Not any model. Just the model with the Minkowski metric an SR, Metrics associated with GR so not result in space-time. The difference is that the coefficients in the metric for SR are constants, whereas the coefficients in the GR metrics (several ahve been proposed) are themselves functions of the coordinates. I have reversed the negative vote as you are quite pleasantly arguing your case. The 'expansion' of space is an interpretation of an emperical (observational) fact, due to Hubble. The 'underlying' - actually applied or chosen - coordinate system are not part of the object we call the universe of space and time - if you like the 'fabric'.

Send me a PM with an email address that can receive jpegs and I will let you have better quality copies. You probably would find it difficult getting hold of the book now in any case.

Of course they would, but I'm not talking about their publicity department. They certainly invented Nylon and ICI held a licence for its manufacture in the UK. But after the war the Sherman Act cause bitterness and much litigation over this licence. Wikipedia will do https://en.wikipedia.org/wiki/Polyethylene_terephthalate#cite_note-9 There is a facebookmemories group you might be interested in for the now defunct ICI fibres. https://www.facebook.com/groups/332552444829415/ Perhaps there is one for Du Pont ?

+1 for your usual clarity of insight.

Yes and no. There are real mechanisms that work using separate rotation axes so it depends upon your frame of reference. Have you heard of Hooke joints or of gimbals for instance ? They are pages scanned as jpegs. click on them to expand to full size then just download from the site page.

@jfoldbar To continue with my four forces theme here is a diagram to show how they affect an aricraft in flight in the three basic different situations. Do you wish to discuss and understand these before worrying about how they are generated ?

+1

But you must have more interesting tales you can share from that time ?? +1 As a matter of interest I recall being taught that Dacron was acquired by DuPont from the pre-ICI who invented the stuff (then called terelene). We understood that the US had nylon and the UK had terelene.

The moderator moved this to the politics forum, but this still remains a scientific website and the rules say the religous section is for the scientific discussion of religous matters. It would be scientific to note and discuss the difference between certain christain denominations in respect of trans-substantiation beliefs, but not to look for justification in believing them or to mock them or supports them.

Nice calm replies to some needlessly imflammatory unscientifc words. +1

Many thanks for all that new information. +1

OK so here is the simplest form of Maths I know for this subject. I have marked the starting point page 289, article 217 - Angular velocites of a body about more than one axis - on the first attachment. You will need some simple calculus and trig.

At my local supermarket

This is all perfectly true but nothing to do with the question in hand which concerns something which is spinning with angular velocity omega about an axis. Your quote concerns the difference between rotation through some finite angle and some infinitesimal angle whereas the angle rotated thorough by spin is unbounded.

Yes, vector combination is quite basic. So, having sent a sphere into 3 separate rotations would have the same effect as a simple rotation along a single axis ? This is completely counter-intuitive. How a single axis would be selected in relation to the other 3 ones then ? Intuition can be a misleading process. The relevant theorem is the original version of Poinsot's theorem which was originally stated in statics, long before vectors were invented. "Every system of of forces can be reduced to a single force and a single moment (torque) , either or both of which can be zero. " This gives rise the the two laws of statics viz that The sum of forces acting in equilibrium is zero. The sum of moments in equilibrium is zero. This can be widened to refer to vectors in more modern parlance and to dynamics where they become https://en.wikipedia.org/wiki/Poinsot's_ellipsoid The point being that any number of rotations can be compounded to become a single rotation resultant, just as any number of forces can be compounded to form a single resultant or net force.

Agreed it is hard to picture. Do you understand resolution of vectors into components ? And that you can equally achieve the same effect as the one vector by (re)combining those components ? Rotations are more complicated motions than linear vectors but the idea is the same.

+1 Perhaps we can put the whole thing down to a 'Samuel Taylor Coleridge' moment - as in Kubla Khan. Perhaps also your imagination would be better directed towards the arts than towards the sciences ?

There is a good account of this and other infinite products for trig functions in the penultimate chapter of Hobson's Plane Trigonometry, entitled Infinite Products, pages 338 - 373.

If you read the wiki article you should note that there are 3 separate angular velocities, [math]{\omega _1};{\omega _2};{\omega _3}[/math] about three mutually perpendicular axes. You can choose any such set of 3 suitable axes, even not perpendicular ones, but the transformation equations normally work the other way because the 3 principal axes of inertia present the formulae in simplest form (diagonal matrices if you work in matrix format). Of course all that is moot for a perfect sphere because any axis is a principal axis and the others follow by symmetry.

Thanks for replying I was just trying to row back a little on the discussion, which was getting rather esoterical. OK so in lower high school (GCSE) enough Physics is introduced for someone to understand but not fully appreciate the mechanics of flight. Anyone with upper high school ( A level) physics should be able to appreciate fully. For some reason nearly all treatments of flight mechanics launch straight into the issue of what keeps an aircraft up. In my opinion this is the hard way to approach it and also leads to a failure to take note of all the forces acting - something the early pioneers failed to do with as result in so many crashes, despite have enormous (by moderns tandards) wing areas. When a physicist talks about "The Four Forces" she means the four fundamental forces of nature and not what we need here. When an aircraft engineer talks about " The Four Forces" he means the four forces that control the mechanics of flight between them. These four forces are Weight, Lift, Drag and Thrust and all are required. (Before you ask, a glider with zero thrust needs a start velocity and eventually fall out of the sky, hopefully in a controlled manner) In my opinion it is best to start with these, just accept they exist, and postpone how they occur until you a happy with knowing how they interact to control flight. This is the approach taken by flight instructors to din these interactions into pilots, so they can 'instinctively' perform the necessary balancing act between the four. I was planning to offer this in more detail when you had responded, but I am about to go out for the day so I will look again this evening.