studiot

Any form of engineering is about compromise and balancing one competing (and often conflicting) requirement against another. If I listed some characteristics to think about for a general engineering product, in no particular order, what would be your reaction? Reliability, Length of service life, Serviceability, Efficiency, Recycleability/Disposal requirements, Safety,

OK I will have a go at a Hitchhiker’s Guide to Hamiltonian-Lagrangian mechanics. If I spread too much jam on it I’m sure Bignose will apply the necessary corrections. First a mathematical observation. I assume you know some elementary calculus. So I will make the statement that every process that can be modelled mathematically by a differential equation can also be formulated as an integral equation. Now Newton’s second law is a differential equation that models the motion of a body as it travels along some trajectory or path. At any point on that path Newton’s Law provides a connection between external forces and the local conditions (at the point) by way of the time rate of change (differential coefficient), to enable us to determine the actual path traversed. I stress this equation is local ie applies individually at each point, but each individual application may be different. Now an alternative view is to ask Is there a function that if applied to the whole path will define that path for us? The answer is yes. There is such a function that we call ‘the action’. If we integrate this action function along any entire proposed path it turns out that the action integral is minimised by using the actual path traversed. This introduces our first Big Name is known as Hamilton’s principle, also called the Principle of Least Action. Now two things. Firstly proving this is the province of some advanced mathematics. Secondly deducing the actual path uses a process ( some more advanced calculus) known as the calculus of variations. I will not attempt either here. The function itself introduces our second Big Name, the Lagrangian. [math]Action = \int_{{t_1}}^{{t_2}} {Ldt} [/math] and for simple conservative fields like gravity the Lagrangian is simply the difference between the kinetic and potential energies L = K – P A parting thought in support of Bignose’ desire for agreement with real world observation. So let us start back with Newton and his law of gravitation. [math]{F_{grav}} = s\frac{{{M_1}{M_2}}}{{{r^2}}}[/math] This states that for two masses there is a force between them proportional to each mass and inversely proportional to the square of the distance between them. s is the constant of proportionality to make this an equation. After it became possible to measure this force, it was noticed that for certain objects there was an additional force in action over and above that given by the gravity equation. This was found to follow the same form (Coulombs law) [math]{F_{elec}} = t\frac{{{Q_1}{Q_2}}}{{{r^2}}}[/math] Well physicists are lazy customers and like to recycle equations rather than introduce new ones. So when magnetism was being investigated another additional force was proposed and the relationship experimentally verified by Michell in 1750. [math]{F_{mag}} = u\frac{{{P_1}{P_2}}}{{{r^2}}}[/math] A quantity known as the pole strength was introduced. Do you notice any similarity? Note I have only used some of the standard symbols for clarity of comparison. Note also that all these three are experimental results. Observations on the physical world.

An excellent suggestion for sevral reasons. Since our last posting here Externet has posted some video references in his thread on this subject, and I replied selecting an axial flow turbine to achieve exactly this. http://www.scienceforums.net/topic/65768-paddle-wheel-calculations-please/ Incidentally one of the advantages of many small installations using horizontal flow is financial. In order to use water head you have to impound water and expend the capital sums to do this (ie build expensive dams or whatever) before there is a penny piece of £return. A small, low cost, installation, placed into an existing flow tidal or river, will immediately start generating and thus providing a £return to help fund a second installation and so on.

ajb Zero can be rather abstractly understood in terms of ring theory. Loosley a ring is a set for which we have addition and multiplication with some natural conditions. In particular we have zero as the additive identity, that is a +0 = 0+a = 0 for all a in the ring. That is zero is the identity element of an abelian group where we write the multiplication as a +. From the properties of the ring you can show that 0.a = a.0 =0. Here . is the binary operation of a monoid. These are the two algebraic interpretations of a zero that I am aware of. The zero ajb describes above is a valid member of the set and is not, I think , the meaning that O'Nero ascribes by the use of the word 'nothingness' (post#5). I think he is referring, not to a member of any set, but to the set which has no members ie the empty set.

If that is so why does Microsoft provide the arrowed buttons? I don't see how the product of two numbers by logarithms is helpful to this homework help.

That is not an equation. You did write an equation out before and I quoted it from your post #3. Your equation tells you what x is equal to in terms of y. That is it gives you a way of calculating x if you know y. What you need is a way of calculating y if you know x. So you rearrange your equation.

It's still an undershot wheel and can never be more than 50% efficient in energy extraction, and then there is the generator efficiency. This one, from the list at the end of the video would be more efficient. http://www.youtube.com/watch?feature=player_embedded&v=dbxLba1EXqs

So you have an equation for x in terms of y So rearrange it to get an equation for y in terms of x Then multiply what ever this is by 3 to get 3y ie 3 times as much. Then take 30% of this. You should notice something interesting about the result.

Have you considered fluid flywheels?

A clear and concise refutation, Bignose +1. metacogitans, you have the germ of a good idea so I am trying to steer you in the appriate direction, because others have trod this path before. However you are trying to minimise the wrong thing, hence my reference to Hamiltonian - Lagrangian mechanics. However I'm sorry to tell you that this approach requires some advanced mathematics and I do not know of a website or book that presents it in elementary terms. Using H-M mechanics leads, amongst other things, to the Schrodinger equation.

Of course it's a problem. Near where I live the river Severn goes up and down 30mtres, twice a day. How do you connect the electrical output from floating paddles to appaatus that has this magnitude of movement? Note I did not say it was impossible, I just said it was a difficulty to overcome. Did you look at the other thread I linked to? There is a deal more information about small installations on rivers there. In the old days watermills were indeed dotted along many rivers, but most had dedicated channels to improve efficiency. Other considerations against simpky 'dipping in are': What about damage to river wildife from the paddles? What about damage from the river in spate including free floating logs etc to the paddle wheels? This is where dedicated side channels score, they can be closed off against flood conditions and netted against fish or debris ingress.

Expressed as a fraction [math]30\% ofy = \frac{{30}}{{100}}y[/math] Can you do it now?

Yes the 'drude model' would be appropriate. http://en.wikipedia.org/wiki/Drude_model

An electric, magnetic or electromagnetic field can exist far from any charge, and even after the effect of the charge can be felt locally, for instance if the emitting star has become a black hole. This field stores energy: the one that the camera feels when seeing the light emitted by the then alive star. And even before this light is detected, standard physics tells it contains energy, whether an electron feels it or not. It's convenient to say so because the energy lost by the emitter's radiation is retrieved at the absorber. In these cases, the field stores energy (0.5*eps*E2, 0.5*B2/mu) without a charged particle to create it nor a charged particle to feel it. Then you have the gravitational effects of light. Negating that the EM field contains energy woud let one run into trouble. You are still avoiding the issue.

You are working towards Lagrangian and Hamiltonian Mechanics. But you need to think in energy terms not force terms. https://www.google.co.uk/search?hl=en-GB&source=hp&q=hamiltonian+mechanics&gbv=2&oq=Hamiltonian&gs_l=heirloom-hp.1.2.0l10.1453.3968.0.7953.11.6.0.5.5.0.125.671.0j6.6.0....0...1ac.1.34.heirloom-hp..0.11.905.0yx_xPQhI7U

Interesting, here's more http://www.dailymail.co.uk/sciencetech/article-2711806/Has-mystery-Siberian-craters-finally-solved-Scientist-claims-created-SINKHOLES-erupted-outwards.html

Does this version help? Said1.pdf

What physical law says that the Lorenz transformation (your starting point) has be be obeyed by a superluminal particle? All we can say with certainty is that letting v = c results in a singularity. We do not know what happens beyond that.

I was the only poster to acknowledge that you might have a point, even if not totally correct in formal mathematics. It's not condescension. It's the rules of this forum. You have posted in maths, where we speculation and theories are not allowed. There is another section for that called speculations, where the rules are more relaxed. Further I asked a question and have since explained why I asked it. Again the rules are quite specific about promoters answering such questions. The whole point of my question is to be able to offer a more detailed answer, because my brief, informal, comment on set theory contains the essence of the mathematical reason why your statement (why shouted in red - this is annoying to many, including myself) is wrong. The reason is simple, there are two mathematical versions of 'nothing', one of which corresponds to your statement above. I had thought that you would be interested in discussing that further.

There are many wild statements about the speed of light and the mathematics of relativity. You should beware of them. The mathematics of relativity does not prohibit superluminal speeds (faster than light). What is does is contain a singularity as a result of division by zero at the the speed of light for any massive object (a massive object, in Physics, is an object with (not necessarily large) rest mass). As you probably know division by zero is not defined in the normal system of mathematics that we use. There is no singularity in the equations at greater than light speeds. This is not an uncommon situation in the mathematics of physics. But what we don't know is if the same equations apply at these greater speeds. If they do there are consequences, not least being that we cannot communicate with anything travelling at these speeds, or even see them. Two examples of other situations where the equations have a barrier like this. Firstly consider the thermal expansion of chocolate, placed in an oven at 15 degrees centigrade and slowly heated. We have an equation that describes the expansion of said chocolate as it heats up, until the chocolate temperature reaches the melting point. At this point the equation fails as the chocolate melts. We can, however, continue to raise the chocolate temperature and the now liquid chocolate expands edit nearly as before, but with a different equation. Secondly there is a quantity known as the specific energy of a flowing liquid described by an equation along the flow surface. Under certain conditions this equation results in a singularity and the flow surface changes abruptly. We do not have a mathematical desciption of the fluid motion in this region. Beyond this region the equations reassert themselves and the flowe surface is again predictable, and the same equations apply again. The phenomenon is known as the hydraulic jump and is used to slow water down at the base of dams to prevent channel scouring.

"For example, i can have a set such as; A={a, b, 4, 3e, boy, &, apple, 0}" That much is true, but the rest is nonsense. The set you describe has negligable significance in Mathematics or Physics. Your mind appears closed to the offerings of others. The word vector has at least four different meanings in Maths, Physics, Computing Science, and Biological Science. I offered you the beginnings of an informal discussion and asked a polite question to find out if it could be tightened up and made more formal. You did not deign to answer. How does this lead to fruitful discussion?

Have you been on holiday? I hope it was somewhere nice. Whilst you were away your question was also developed in another thread. http://www.scienceforums.net/topic/65768-paddle-wheel-calculations-please/

Aircraft carriers are often tilted an/or facing the wrong way. I don't have the knowledge, but what we need is a pilot with carrier experience to tell us his/her thoughts.

Actually. O'Nero your thoughts are not far from the truth. There are in fact several key ideas or words that differ in mathematics and physics. Are you familiar with set theory and the construction of the real numbers from elementary sets? Informally mathematicians distinguish two versions of 'nothing'. Null and Zero. Consider sets of numbers. There is a set that has one member, a set that has two members, as set that has three members and so on. That is {a} ; (a,b}; {a,b,c} and so on. The letters a, b, c etc can stand for any number so b could be the number that solves the equation 2+2=b (ie 4) a could be the number that solves the equation x + a = x for all numbers, x. That is another name for zero. It must be a valid number since it solves an equation. So the set {0} is a set that contains just one number zero. But in additions to the sets above there is another set of numbers that has no members whasoever. This is called the empty set or the null set {} and is different from {0}. Does this help?

Yes, I agree that's the way it works, but that is not the point I have been trying to make. So I will try again. In an otherwise empty universe Take 1kg of mass. I can calculate the total energy in Joules I would receive if I were able to convert that to energy, using the expression E=mc2 Now compare that with charge In an otherwise empty universe Take 1 coulomb of charge. As far as i know there is no formula, similar to the mass one, to replace all that charge with a specific quantity of Joules. Worse, in the mass universe part only of the mass may be converted to energy, leaving a smaller amount of mass. But in the charge universe there is I know of no corresponding process that can partly destroy charge. Now in each universe if you introduce a second entity In the mass universe there will be gravitational potential energy between the two masses. In the charge universe there will be electric potential energy between the two charges. So they are more similar here.