On Transverse Vibrations of a Rotating Disk of Uniform Strength

1992 ◽  
Vol 59 (1) ◽  
pp. 234-235 ◽  
Author(s):  
Ugˇur Gu¨ven
Keyword(s):  
Closed Form ◽  
Hypergeometric Functions ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Transverse Motion ◽  
Confluent Hypergeometric Functions ◽  
Transverse Vibrations ◽  
Uniform Strength

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.

scholarly journals Closed-Form Solution for the Solow Model with Constant Migration

2015 ◽  
Vol 16 (2) ◽  
pp. 147
Author(s):  
João Plínio Juchem Neto ◽  
Julio Cesar Ruiz Claeyssen ◽  
Daniele Ritelli ◽  
Giovanni Mingari Scarpello
Keyword(s):  
Closed Form ◽  
Migration Rate ◽  
Hypergeometric Functions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Solow Model ◽  
Emigration Rate ◽  
Economic Growth Model ◽  
Stability Issues ◽  
Douglas Production Function

In this work we deal with the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss' Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

2020 ◽  
Vol 44 (1) ◽  
pp. 20-50
Author(s):  
Surja Deka ◽  
Ashis Mallick ◽  
Pratyush P. Behera ◽  
Prakash Thamburaja
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Functionally Graded

scholarly journals A Novel Approach to Develop a Closed-Form Solution for MHD Flow Induced by a Rotating Disk

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 124410-124416
Author(s):  
Zeshan Zulifqar ◽  
Azad Akhter Siddiqui ◽  
Meraj Mustafa Hashmi
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Form Solution ◽  
Novel Approach

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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