Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications
Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all...
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| Autor*in: |
Zhao, Xiao-Min [verfasserIn] Chen, Ye-Hwa [verfasserIn] Zhao, Han [verfasserIn] Dong, Fang-Fang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Chinese Journal of Mechanical Engineering - Chinese Mechanical Engineering Society, 2012, 31(2018), 1 vom: 24. Dez. |
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| Übergeordnetes Werk: |
volume:31 ; year:2018 ; number:1 ; day:24 ; month:12 |
| Links: |
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| DOI / URN: |
10.1186/s10033-018-0310-x |
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SPR008134103 |
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| 520 | |a Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. | ||
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10.1186/s10033-018-0310-x doi (DE-627)SPR008134103 (SPR)s10033-018-0310-x-e DE-627 ger DE-627 rakwb eng Zhao, Xiao-Min verfasserin aut Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. Udwadia–Kalaba Equation (dpeaa)DE-He213 Mechanical system (dpeaa)DE-He213 Constraint (dpeaa)DE-He213 Moore–Penrose inverse (dpeaa)DE-He213 Chen, Ye-Hwa verfasserin aut Zhao, Han verfasserin aut Dong, Fang-Fang verfasserin aut Enthalten in Chinese Journal of Mechanical Engineering Chinese Mechanical Engineering Society, 2012 31(2018), 1 vom: 24. Dez. (DE-627)SPR008124000 nnns volume:31 year:2018 number:1 day:24 month:12 https://dx.doi.org/10.1186/s10033-018-0310-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 31 2018 1 24 12 |
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10.1186/s10033-018-0310-x doi (DE-627)SPR008134103 (SPR)s10033-018-0310-x-e DE-627 ger DE-627 rakwb eng Zhao, Xiao-Min verfasserin aut Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. Udwadia–Kalaba Equation (dpeaa)DE-He213 Mechanical system (dpeaa)DE-He213 Constraint (dpeaa)DE-He213 Moore–Penrose inverse (dpeaa)DE-He213 Chen, Ye-Hwa verfasserin aut Zhao, Han verfasserin aut Dong, Fang-Fang verfasserin aut Enthalten in Chinese Journal of Mechanical Engineering Chinese Mechanical Engineering Society, 2012 31(2018), 1 vom: 24. Dez. (DE-627)SPR008124000 nnns volume:31 year:2018 number:1 day:24 month:12 https://dx.doi.org/10.1186/s10033-018-0310-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 31 2018 1 24 12 |
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10.1186/s10033-018-0310-x doi (DE-627)SPR008134103 (SPR)s10033-018-0310-x-e DE-627 ger DE-627 rakwb eng Zhao, Xiao-Min verfasserin aut Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. Udwadia–Kalaba Equation (dpeaa)DE-He213 Mechanical system (dpeaa)DE-He213 Constraint (dpeaa)DE-He213 Moore–Penrose inverse (dpeaa)DE-He213 Chen, Ye-Hwa verfasserin aut Zhao, Han verfasserin aut Dong, Fang-Fang verfasserin aut Enthalten in Chinese Journal of Mechanical Engineering Chinese Mechanical Engineering Society, 2012 31(2018), 1 vom: 24. Dez. (DE-627)SPR008124000 nnns volume:31 year:2018 number:1 day:24 month:12 https://dx.doi.org/10.1186/s10033-018-0310-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 31 2018 1 24 12 |
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10.1186/s10033-018-0310-x doi (DE-627)SPR008134103 (SPR)s10033-018-0310-x-e DE-627 ger DE-627 rakwb eng Zhao, Xiao-Min verfasserin aut Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. Udwadia–Kalaba Equation (dpeaa)DE-He213 Mechanical system (dpeaa)DE-He213 Constraint (dpeaa)DE-He213 Moore–Penrose inverse (dpeaa)DE-He213 Chen, Ye-Hwa verfasserin aut Zhao, Han verfasserin aut Dong, Fang-Fang verfasserin aut Enthalten in Chinese Journal of Mechanical Engineering Chinese Mechanical Engineering Society, 2012 31(2018), 1 vom: 24. Dez. (DE-627)SPR008124000 nnns volume:31 year:2018 number:1 day:24 month:12 https://dx.doi.org/10.1186/s10033-018-0310-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 31 2018 1 24 12 |
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10.1186/s10033-018-0310-x doi (DE-627)SPR008134103 (SPR)s10033-018-0310-x-e DE-627 ger DE-627 rakwb eng Zhao, Xiao-Min verfasserin aut Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. Udwadia–Kalaba Equation (dpeaa)DE-He213 Mechanical system (dpeaa)DE-He213 Constraint (dpeaa)DE-He213 Moore–Penrose inverse (dpeaa)DE-He213 Chen, Ye-Hwa verfasserin aut Zhao, Han verfasserin aut Dong, Fang-Fang verfasserin aut Enthalten in Chinese Journal of Mechanical Engineering Chinese Mechanical Engineering Society, 2012 31(2018), 1 vom: 24. Dez. (DE-627)SPR008124000 nnns volume:31 year:2018 number:1 day:24 month:12 https://dx.doi.org/10.1186/s10033-018-0310-x kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 31 2018 1 24 12 |
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Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. |
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Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. |
| abstract_unstemmed |
Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. |
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Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications |
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Chen, Ye-Hwa Zhao, Han Dong, Fang-Fang |
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