scholarly journals Oscillation of a pendulum subject to a horizontal trajectory with different kinds of motion

2019 ◽  
pp. 17-29
Author(s):  
Rodolfo Espindola-Heredia ◽  
Gabriela Del Valle ◽  
Damián Muciño-Cruz ◽  
Guadalupe Hernandez-Morales
Keyword(s):  
Horizontal Plane ◽  
Wireless Sensors ◽  
Equations Of Motion ◽  
First Integrals ◽  
Experimental Results ◽  
Lagrangian Mechanics ◽  
Experimental Prototype ◽  
Oscillatory Movement ◽  
Spatial Coordinates ◽  
Rigid Rod

In the children's movie The Incredibles there is a scene where Mr Incredible faces Bomb Voyage, while Incredi Boy wants to help Mr Incredible, Incredi Boy flies with Mr Incredible, who holds on to the hero's cloak, affecting Incredi Boy’s flight plan. To understand how an oscillatory movement affects non-oscillatory movement, an experimental prototype was constructed with a particle of mass m, attached to a rigid rod and without mass of length l, to a swivel of negligible mass, which was subject to a mass M. The swivel always remained on a horizontal plane, allowing the oscillatory movement of mass m. Experimental results were obtained by means of wireless sensors which recorded the spatial coordinates of the mass m. Using Lagrangian mechanics we obtained the equations of motion and expressed the possible first integrals of movement, when the movement of the mass M was: linear uniform (ULM), uniformly accelerated, (UAM), uniform circular (UCM), accelerated circular (ACM) and forced circular (FCM). The dynamics were analyzed, the equations of movement obtained, they were solved numerically, and the experimental results were compared to theoretical and numerical results.

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

Amplitude propagation in slowly varying trains of shear-flow instability waves

1986 ◽  
Vol 170 ◽  
pp. 21-51 ◽  
Author(s):  
J. M. Russell
Keyword(s):  
Variational Principles ◽  
Flow Instability ◽  
Near Field ◽  
Equations Of Motion ◽  
Wave Action ◽  
Small Disturbance ◽  
Instability Waves ◽  
Action Density ◽  
Spatial Coordinates ◽  
Shear Flow Instability

The analog of Whitham's law of conservation of wave action density is derived in the case of Rayleigh instability waves. The analysis allows for wave propagation in two space dimensions, non-unidirectionality of the background flow velocity profiles and weak horizontal nonuniformity and unsteadiness of those profiles. The small disturbance equations of motion in the Eulerian flow description are subject to a change of dependent variable in which the new variable represents the pressure-driven part of a disturbance material coordinate function as a function of the Cartesian spatial coordinates and time. Several variational principles expressing the physics of the small disturbance equations of motion are presented in terms of this new variable. A law of conservation of ‘bilinear wave action density’ is derived by a method intermediate between those of Jimenez and Whitham (1976) and Hayes (1970a). The distinction between the observed square amplitude of an amplified wavetrain and the wave action density is discussed. Three types of algebraic focusing are discussed, the first being the far-field ‘caustics’, the second being near-field ‘movable singularities’, and the third being a focusing mechanism due to Landahl (1972) which we here derive under somewhat weaker hypotheses.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

scholarly journals Design and Experiment of Banana De-Handing Device Based on Symmetrical Shape Deployable Mechanism

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 415
Author(s):  
Jie Guo ◽  
Mohui Jin ◽  
Jieli Duan ◽  
Jun Li ◽  
Han Fu ◽  
...  
Keyword(s):  
Experimental Results ◽  
Kinematics Analysis ◽  
Experimental Prototype ◽  
Symmetrical Shape ◽  
Length Width ◽  
Deployable Mechanism

Aiming at the problem that the banana de-handing device has poor radial deployment to the banana bunch stalk during the mechanized banana de-handing procedure, this paper presented a ring deployable mechanism based on a set of planar seven-bar linkages. It consists of multiple basic deployable units, which has great folding/deploying performance and is suitable for manufacturing a banana de-handing device, the diameter of which can be variably larger. The kinematics analysis of the mechanism was done, and the trajectory in space was obtained. When the mechanism is fully deployed, the diameter is 164 mm. The ratio of the folded height to the deployed diameter is 0.732, the ratio of the folded diameter to the deployed diameter is 0.262, and the ratio of the folded volume to the maximum of the deployed volume is 0.069. An experimental prototype of 500, 500, and 768 mm in length, width, and height was manufactured, and the deploying performance was analyzed to show the feasibility. Finally, experimental results show that 71.43% of the banana hands are de-handed successfully. The mechanism has a great deploying effect on banana bunch stalk, and the quality of the banana crown incision is good.

Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes

2015 ◽  
Vol 38 ◽  
pp. 1560072 ◽  
Author(s):  
Ugur Camci
Keyword(s):  
Equations Of Motion ◽  
Complete Characterization ◽  
First Integrals ◽  
Geodesic Motion ◽  
Geodesic Equations ◽  
Gauge Symmetries ◽  
Geodesic Equations Of Motion

In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for [Formula: see text] of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.

A NEW AND SIMPLE CHAOS TOY

2002 ◽  
Vol 12 (08) ◽  
pp. 1843-1857 ◽  
Author(s):  
ERIK M. BOLLT ◽  
AARON KLEBANOFF
Keyword(s):  
Ball Bearing ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Future Application ◽  
Lagrangian Mechanics ◽  
Smale Horseshoe ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Bicycle Wheel

We present two new, and perhaps the simplest yet, mechanical chaos demonstrations. They are both designed based on a recipe of competing nonlinear oscillations. One of these devices is simple enough that using the provided description, it can be built using a bicycle wheel, a piece of wood routed with an elliptical track, and a ball bearing. We provide a thorough Lagrangian mechanics based derivation of equations of motion, and a proof of chaos based on showing the existence of an embedded Smale horseshoe using Melnikov's method. We conclude with discussion of a future application.

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