Period estimate for the simple pendulum using optimization theory

1988 ◽  
Vol 28 (3) ◽  
pp. 179-190
Author(s):  
Randall D. Peters
1987 ◽  
Vol 15 (1) ◽  
pp. 3-29 ◽  
Author(s):  
K. Yamagishi ◽  
M. Togashi ◽  
S. Furuya ◽  
K. Tsukahara ◽  
N. Yoshimura

Abstract The Rolling Contour Optimization Theory (RCOT) can lead to improved steering, fuel efficiency, riding comfort, and braking performance of tires relative to those of conventional shape. The conventional shape has been guided by natural equilibrium profiles, while the RCOT technology shape is guided by that of the tire in motion. This reduces useless distortions caused by running the tire under load. The RCOT design focuses on the distribution of belt and sidewall tension in the tire. Controlling tension in the belt and carcass area while the tire is in motion was the key to creating this new tire shape.


Author(s):  
Alfonso Sorrentino

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.


Author(s):  
Dan J. Bodoh

Abstract The growth of the Internet over the past four years provides the failure analyst with a new media for communicating his results. The new digital media offers significant advantages over analog publication of results. Digital production, distribution and storage of failure analysis results reduces copying costs and paper storage, and enhances the ability to search through old analyses. When published digitally, results reach the customer within minutes of finishing the report. Furthermore, images on the computer screen can be of significantly higher quality than images reproduced on paper. The advantages of the digital medium come at a price, however. Research has shown that employees can become less productive when replacing their analog methodologies with digital methodologies. Today's feature-filled software encourages "futzing," one cause of the productivity reduction. In addition, the quality of the images and ability to search the text can be compromised if the software or the analyst does not understand this digital medium. This paper describes a system that offers complete digital production, distribution and storage of failure analysis reports on the Internet. By design, this system reduces the futzing factor, enhances the ability to search the reports, and optimizes images for display on computer monitors. Because photographic images are so important to failure analysis, some digital image optimization theory is reviewed.


1913 ◽  
Vol 7 (108) ◽  
pp. 189
Author(s):  
G. Greenhill
Keyword(s):  

1972 ◽  
Vol 79 (4) ◽  
pp. 348-355
Author(s):  
Fred Brauer
Keyword(s):  

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