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- : Eponymously discovered by Faraday[1], Faraday Waves are standing waves on a fluid caused by vertical oscillator ...t \left(\nabla\vec{v} + \nabla\vec{v}^T \right)+ \frac{1}{Fr}F(cos(2\pi t)-1)\mathbf{j}</math>28 KB (4,305 words) - 09:57, 12 January 2012
- #REDIRECT [[Group-1 (2010)]]28 bytes (2 words) - 22:31, 28 November 2011
- 29 bytes (3 words) - 22:31, 28 November 2011
- ...determines a smooth vector field on <math>\mathbb{R}^{2}\times \mathbb{S}^{1}</math> (a 3 dimensional space) and hence truly chaotic behavior is possibl ...nd the trajectories are curves of constant energy <math>E(x,\dot{x})=\frac{1}{2}\dot{x}^{2}+V(x)</math>. In this case it is easy to see that we have a s25 KB (4,001 words) - 22:50, 28 October 2014
- [[File:Shear.png | thumb | 300px | Figure 1: Force gradient viewed from above.]] Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's chirality, <math>g</mat10 KB (1,538 words) - 16:25, 12 December 2014
- <!--fig example [[File:NAME.png | thumb | 300px | Figure 1: FIG NAME.]]--> [1] ...574 bytes (64 words) - 12:06, 18 April 2023
Page text matches
- <!--fig example [[File:NAME.png | thumb | 300px | Figure 1: FIG NAME.]]--> [1] ...574 bytes (64 words) - 12:06, 18 April 2023
- <!--fig example [[File:NAME.png | thumb | 300px | Figure 1: FIG NAME.]]--> [1] ...570 bytes (64 words) - 12:07, 18 April 2023
- * [[Media: Rijke Mitchell Passarelli.pdf | Final report 1]]391 bytes (60 words) - 11:19, 29 January 2021
- *[[Media: Fire Benjamin Musci.pdf | Final report 1]]437 bytes (67 words) - 11:17, 29 January 2021
- * [[Media:Faraday Alejandro Escontrela.pdf | Final report 1]]452 bytes (67 words) - 11:18, 29 January 2021
- * [[Media: Vortex Jaesung Jeon.pdf | Final report 1]]441 bytes (67 words) - 11:18, 29 January 2021
- * [[Media: Metronome Aris Kanellopoulos.pdf | Final report 1]]474 bytes (68 words) - 11:20, 29 January 2021
- -x & |x| < 1 \\ [-1 + \beta(|x| - 1)sgn(x) & 1 < |x| < 10 \\8 KB (1,234 words) - 14:27, 17 October 2011
- ===Assignment 1=== ...rom Strogatz, 2nd edition: 2.2.7, 2.3.3, 2.4.2, 2.5.6G, 2.6.2G, 2.8.8, 3.1.1, 3.4.11, 3.4.14, 3.5.6G, 3.6.6. Problems with a G at the end are problems a7 KB (1,124 words) - 11:36, 30 October 2014
- [[File:ScreenHunter_92_Sep._21_18.03.jpg | thumb | 300px | Simple 1-D freedom jumping robot]] ...or analyzed using various accepted techniques. The jumping robot exhibited 1-cycle, 2-cycle, 3-cycle and chaotic motion, which was mostly consistent wit6 KB (970 words) - 14:35, 24 September 2012
- Jan 9: Lecture 1, intro to the subject Feb 1: Lecture 6, imperfect bifurcations (Chap 3)3 KB (386 words) - 11:31, 18 April 2023
- {|cellpadding="5" cellspacing="0" border="1" width="60%" | Faraday waves ([[Group 1]] requested this) and Plinko dynamics4 KB (570 words) - 16:31, 17 October 2011
- {|cellpadding="5" cellspacing="0" border="1" width="60%" ...Fire.pdf |Presentation]]. [[Media: Fire Benjamin Musci.pdf | Final report 1]], [[Media: Match Lezheng Fang.pdf | Final report 2]], [[Media: Match Mateo10 KB (1,348 words) - 11:25, 18 April 2023
- ...sions. As such small differences in initial conditions grow exponentially [1]. Due to its simplicity and rich dynamical behavior, this system is widely ...d the second arm (vertical axis) from -180 to 180 degrees in approximately 1 degree steps. It is overlaid with experimental data points of time to flip,6 KB (954 words) - 18:11, 23 September 2012
- \frac{A\omega^2}{g} [\sin(\omega t) + c^2 \sin(c \omega t)] &\geq 1 x_b(t) = &x_p(t_0) - x_p(t) + \dot{x}_p(t_0)(t-t_0) - 1/2 g(t-t_0)^2 \notag\\15 KB (2,451 words) - 09:59, 12 January 2012
- ...isplaystyle{d\theta_{i}\over{dt}} = \omega_t + {K\over{N}}\sum\limits_{j = 1}^{N} \sin(\theta_j - \theta_i)$$ (i) $\displaystyle{d\phi \over{dt}} = {1\over{T}}$ models the change of phase of the oscillator22 KB (3,469 words) - 22:50, 28 October 2014
- \documentclass[twocolumn,aip,cha]{revtex4-1} %\includegraphics[scale=1]{Fig.jpg}6 KB (870 words) - 10:20, 11 September 2012
- [[File:Shear.png | thumb | 300px | Figure 1: Force gradient viewed from above.]] Where <math>\chi = \{ 0,-1,1 \}</math> indicates the direction of the particle's chirality, <math>g</mat10 KB (1,538 words) - 16:25, 12 December 2014
- === Single Inverted Pendulum, $N = 1$ === \epsilon = 0.450 + 1.799/\Omega^{2}27 KB (4,171 words) - 10:01, 12 January 2012
- ...determines a smooth vector field on <math>\mathbb{R}^{2}\times \mathbb{S}^{1}</math> (a 3 dimensional space) and hence truly chaotic behavior is possibl ...nd the trajectories are curves of constant energy <math>E(x,\dot{x})=\frac{1}{2}\dot{x}^{2}+V(x)</math>. In this case it is easy to see that we have a s25 KB (4,001 words) - 22:50, 28 October 2014
- \dot{\theta}_k(t) = \omega + \frac{k}{n} \sum_{i=1}^n \sin\left(\theta_i(t) - \theta_k(t)\right). [[File:Coupled_Oscillators_11.png | thumb | 300px | right | Figure 1: Phases of 11 Coupled Harmonic Oscillators.]]13 KB (1,911 words) - 19:20, 12 December 2014
- ...particles (~10nm) that react paramagnetically to a uniform magnetic field [1]. The fluid becomes magnetized in the presence of a magnetic field and un- ...nly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied.21 KB (3,267 words) - 10:00, 12 January 2012
- ...nline&aid=283922 | journal=Journal of Fluid Mechanics | volume=526 | pages=1-17}}</ref>. However, it is not very precise, and gives very little informat ...& Fuchikami<ref name="K&F" /> adopt a set of geometrized units such that g=1. For water at twenty degrees centigrade, these units are l0=0.27 cm, t0=0.029 KB (4,574 words) - 10:00, 12 January 2012
- ...the stutter jump (dashed). A transition point occurs at $\alpha \approx 0.1$. Below this value, the stutter jump performs better. {| border="1" class="wikitable"12 KB (1,977 words) - 11:52, 12 December 2014
- [[File:built_chua.png|thumb|400px|alt=text|Figure 1: Two Chua Circuits on a single breadboard]] ...plicated the circuit diagram in Figure (1). It has four major components: (1) a variable resistor, whose resistance acts as the control variable, (2) tw22 KB (3,535 words) - 22:52, 28 October 2014
- : Eponymously discovered by Faraday[1], Faraday Waves are standing waves on a fluid caused by vertical oscillator ...t \left(\nabla\vec{v} + \nabla\vec{v}^T \right)+ \frac{1}{Fr}F(cos(2\pi t)-1)\mathbf{j}</math>28 KB (4,305 words) - 09:57, 12 January 2012
- 1. What amplitudes and frequencies of periodic forcing allow the inverted pen <math>\frac{\delta v}{\delta t}=-\frac{v}{Q \Omega}-\left[\frac{1}{\Omega^{2}}-\epsilon*cn(t,m)\right]*\sin{\theta}</math>9 KB (1,372 words) - 17:47, 23 September 2012
- ...d the aggregate statistics of the outcomes based on the starting position [1,2]. These analyses assume that each puck-pin interaction can only result i ...t on the puck velocity. The acceleration from the magnets is modeled as a 1/r^2 function, which should be valid for small magnets spaced far apart. Th30 KB (4,949 words) - 09:59, 12 January 2012
- Where $x_i$ is the state of an oscillator with $x_i \in [0,1]$, $S_0$ is a property of the x_i = 1 \Rightarrow \; x_j(t^+) = \eta + x_j(t) \quad \forall j \neq i27 KB (4,253 words) - 22:52, 28 October 2014
- ...tup is shown to the right, with the metronomes always being placed along a 1-dimensional array. \ddot\phi_j+b\dot\phi_j+\frac{g}{l}\sin\phi_j=-\frac{1}{l}\ddot X \cos\phi_j+F_j21 KB (3,282 words) - 10:00, 12 January 2012
- \scriptsize{L = \frac{1}{2}\dot{q}^TM\dot{q}-V(q)} Figures 1 thru 3 demonstrate that the active time of the end bobs increased as the As18 KB (2,990 words) - 21:32, 17 February 2015