Chaos | Chapter 5 : Billiards - Duhem's bull

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Chaos | Chapter 5 : Billiards - Duhem's bull
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École Normale Supérieure de Lyon (ENS-Lyon)

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Subject Area
Area Complex (psychology) Weight Surface Direction (geometry) Projective plane Model theory Line (geometry) Regular graph Parabola Mathematics Friction Velocity Collision Mathematician Position operator Stability theory
Cue sports Trajectory Matching (graph theory) Infinity Similarity (geometry) Game theory Mathematician Table (information) Initial value problem Near-ring Ellipse
Trajectory Complex (psychology) Friction Many-sorted logic Direction (geometry) Game theory Condition number
Point (geometry) Cue sports Area Trajectory Dot product Rational number Multiplication sign Real number Direction (geometry) Mereology Arithmetic mean Finite set Velocity Physicist Right angle Table (information) Initial value problem Position operator
Mathematics Quantum state Model theory Chaos (cosmogony)
Mathematics Chaos (cosmogony)
understanding of celestial objects it is an old dream the some people say they can read their best start please but we predict collisions between planets it I what could gravitation projects some planets the With or should we rather expect and the stability of the solar system the the but he's a delicate question the did but as always in mathematics but faced with a problem that is too difficult is that the 1st look for simpler situation Henry man for consider this parabolic the and the the if we launch a ball is subject to its weight direction for which we see that the pond is analogous to that of a man who tried to stop his movement seems to regular model complex solar system with let's take a boat that is the of the ball was still subject to its way into the reaction from now the movement is really and if you can in let's take away the weight of the box but keep the reaction force of the surface but this into G-8 due him the philosopher of science presenting the work the mathematician other Mark published in 1898 an article entitled on surface With opposite the material maths slide that it is more friction candles he describes her line that John Mitchell called but under consideration when the initial position on matters and the direction of its initial velocity the geodesic defined area you can do why am I he
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president near and ate I know still To here also 2 balls with similar initial conditions have trajectories that remained close together it is as if we were trying to death 6 on the 4th without but that's head of a
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friction there are 3 circular obstacle let's call them MCA now it's as if we are observing Ojeda 6 on us with 3 let's take a ball and she if we well trajectory and then see that then be In periodic trying to get but the other periodic audits there was beautiful he said but if you choose any work Rick the 3 letters a he under the condition the consecutive letters are different for example ABC ABC C then there is a periodic trajectories visits the bumper successively indeed ordered dictated by the wording question that you see complexity of the situation for each word there's a periodic trajectories and there are lots of sorts for example the word gay scene being seen being seen Is it trajectory that pertains to hit us once every 11 rebounds it will hit on Burke Of course we must aim precisely very very precise the but I the an all this makes 1 think
of the real numbers what we regularly some of the periodic these are exactly the rational as an example 123 over 999 it 0 . 1 2 3 1 2 3 1 2 3 and so on while To over 7 is equal to 0 . 2 8 5 7 1 2 a time 7 1 2 8 5 7 1 and such a rational number when it does not they for example are table is similar some trajectories chaotic an are described by periodic word and the letters do In scene others In are described by means still others visit ATP concede a finite number of times and then they escaped to never to return here is to OEMs that
are geodesic the tools to the removal of the area they are all those dots coming back from nearly ended she far away from through Song keep turning around the right hole another those Toronto left are all those more complicated 1 I 1 hole we stood here are the photo in Hong Kong there would be geodesic that will go to infinity 1 by finding the right others like kind at home the imagine the His always been knickers companion suddenly deciding to shoot on Twitter at noon despite this complication before I know it was actually accuracy the initial position on the part of the former head of his boat and the direction of the initial velocity the geodesic that these point with foot during its movement wouldn't be fixed it would be quite different initial conditions and not known mathematical but Park I appreciate the subtlety not mathematically practically give watch these it did at the same point start almost in the same direction they follow almost then a separate green red and blue 6 have completely different future if the war lounged on the Salafist questions from a position that is given Joe Mexican With a speed that is given Joe Maddock could then mathematical deductions can determine the trajectory of the in determining this trajectory but for the physicist these deductions for ever you should so far all of this applies to GSA billiard ball trajectory can this be applied the everyday life of for instance the movement of the
planets the the but the question of telling my future it's still there


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