Analytical Lorentz Force Model Between 1-D Linear Currents in Arbitrary Relative Positions and Directions
We derive an analytical formula for the Lorentz force and torque between 1-D linear current elements in arbitrary relative positions explicitly without remaining integral. A circuit is represented as the links of linear elements, and the force and torque on an element are represented as equivalent n...
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| Veröffentlicht in: | IEEE transactions on magnetics 2018-08, Vol.54 (8), p.1-16 |
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| container_title | IEEE transactions on magnetics |
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| creator | Kawai, Tsubasa Inamori, Takaya Hori, Koichi |
| description | We derive an analytical formula for the Lorentz force and torque between 1-D linear current elements in arbitrary relative positions explicitly without remaining integral. A circuit is represented as the links of linear elements, and the force and torque on an element are represented as equivalent nodal forces on either side of it. We then treat the circuit as a link mechanism. Furthermore, we consider the singularity that appears in connected elements in a single circuit due to zero distance and avoid it using an approximation with a small radius. This singularity treatment makes the formula applicable even for calculation of the partial force from the entire circuit. Since the formula does not require numerical integration, it can reduce computation time. The accuracy of the approximation is also evaluated by comparing our calculations with the existing experimental results in the literature and numerical integrations. |
| doi_str_mv | 10.1109/TMAG.2018.2841382 |
| format | Article |
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A circuit is represented as the links of linear elements, and the force and torque on an element are represented as equivalent nodal forces on either side of it. We then treat the circuit as a link mechanism. Furthermore, we consider the singularity that appears in connected elements in a single circuit due to zero distance and avoid it using an approximation with a small radius. This singularity treatment makes the formula applicable even for calculation of the partial force from the entire circuit. Since the formula does not require numerical integration, it can reduce computation time. The accuracy of the approximation is also evaluated by comparing our calculations with the existing experimental results in the literature and numerical integrations.</description><identifier>ISSN: 0018-9464</identifier><identifier>EISSN: 1941-0069</identifier><identifier>DOI: 10.1109/TMAG.2018.2841382</identifier><identifier>CODEN: IEMGAQ</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>1-D current element ; analytical integration ; Analytical models ; Approximation ; Circuits ; Force ; Lorentz covariance ; Lorentz force ; Magnetic circuits ; Magnetic forces ; Magnetism ; Mathematical analysis ; Mathematical model ; Mathematical models ; Numerical integration ; singularity treatment ; Torque</subject><ispartof>IEEE transactions on magnetics, 2018-08, Vol.54 (8), p.1-16</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2018</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-2907bc697c982058b3c09ccf4dba73ba106a42f7e2954701b240f599a66765b63</citedby><cites>FETCH-LOGICAL-c359t-2907bc697c982058b3c09ccf4dba73ba106a42f7e2954701b240f599a66765b63</cites><orcidid>0000-0003-3109-8285 ; 0000-0002-0910-280X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8383715$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>315,781,785,797,27928,27929,54762</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/8383715$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Kawai, Tsubasa</creatorcontrib><creatorcontrib>Inamori, Takaya</creatorcontrib><creatorcontrib>Hori, Koichi</creatorcontrib><title>Analytical Lorentz Force Model Between 1-D Linear Currents in Arbitrary Relative Positions and Directions</title><title>IEEE transactions on magnetics</title><addtitle>TMAG</addtitle><description>We derive an analytical formula for the Lorentz force and torque between 1-D linear current elements in arbitrary relative positions explicitly without remaining integral. A circuit is represented as the links of linear elements, and the force and torque on an element are represented as equivalent nodal forces on either side of it. We then treat the circuit as a link mechanism. Furthermore, we consider the singularity that appears in connected elements in a single circuit due to zero distance and avoid it using an approximation with a small radius. This singularity treatment makes the formula applicable even for calculation of the partial force from the entire circuit. Since the formula does not require numerical integration, it can reduce computation time. The accuracy of the approximation is also evaluated by comparing our calculations with the existing experimental results in the literature and numerical integrations.</description><subject>1-D current element</subject><subject>analytical integration</subject><subject>Analytical models</subject><subject>Approximation</subject><subject>Circuits</subject><subject>Force</subject><subject>Lorentz covariance</subject><subject>Lorentz force</subject><subject>Magnetic circuits</subject><subject>Magnetic forces</subject><subject>Magnetism</subject><subject>Mathematical analysis</subject><subject>Mathematical model</subject><subject>Mathematical models</subject><subject>Numerical integration</subject><subject>singularity treatment</subject><subject>Torque</subject><issn>0018-9464</issn><issn>1941-0069</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kF1LwzAUhoMoOD9-gHgT8LrzJE3a5nJubgodiszrkGankFHbmWTK_PW2bnh1eDnPe-A8hNwwGDMG6n61nCzGHFgx5oVgacFPyIgpwRKATJ2SEfSrRIlMnJOLEDZ9FJLBiLhJa5p9dNY0tOw8tvGHzjtvkS67NTb0AeM3YktZMqOla9F4Ot35gQvUtXTiKxe98Xv6ho2J7gvpaxdcdF0bqGnXdOY82r94Rc5q0wS8Ps5L8j5_XE2fkvJl8TydlIlNpYoJV5BXNlO5VQUHWVSpBWVtLdaVydPKMMiM4HWOXEmRA6u4gFoqZbIsz2SVpZfk7nB367vPHYaoN93O918GzRnLQQKIgWIHyvouBI-13nr30T-iGejBqB6M6sGoPhrtO7eHjkPEf75IizRnMv0FhN5xLw</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Kawai, Tsubasa</creator><creator>Inamori, Takaya</creator><creator>Hori, Koichi</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-3109-8285</orcidid><orcidid>https://orcid.org/0000-0002-0910-280X</orcidid></search><sort><creationdate>20180801</creationdate><title>Analytical Lorentz Force Model Between 1-D Linear Currents in Arbitrary Relative Positions and Directions</title><author>Kawai, Tsubasa ; Inamori, Takaya ; Hori, Koichi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-2907bc697c982058b3c09ccf4dba73ba106a42f7e2954701b240f599a66765b63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>1-D current element</topic><topic>analytical integration</topic><topic>Analytical models</topic><topic>Approximation</topic><topic>Circuits</topic><topic>Force</topic><topic>Lorentz covariance</topic><topic>Lorentz force</topic><topic>Magnetic circuits</topic><topic>Magnetic forces</topic><topic>Magnetism</topic><topic>Mathematical analysis</topic><topic>Mathematical model</topic><topic>Mathematical models</topic><topic>Numerical integration</topic><topic>singularity treatment</topic><topic>Torque</topic><toplevel>online_resources</toplevel><creatorcontrib>Kawai, Tsubasa</creatorcontrib><creatorcontrib>Inamori, Takaya</creatorcontrib><creatorcontrib>Hori, Koichi</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on magnetics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kawai, Tsubasa</au><au>Inamori, Takaya</au><au>Hori, Koichi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical Lorentz Force Model Between 1-D Linear Currents in Arbitrary Relative Positions and Directions</atitle><jtitle>IEEE transactions on magnetics</jtitle><stitle>TMAG</stitle><date>2018-08-01</date><risdate>2018</risdate><volume>54</volume><issue>8</issue><spage>1</spage><epage>16</epage><pages>1-16</pages><issn>0018-9464</issn><eissn>1941-0069</eissn><coden>IEMGAQ</coden><abstract>We derive an analytical formula for the Lorentz force and torque between 1-D linear current elements in arbitrary relative positions explicitly without remaining integral. A circuit is represented as the links of linear elements, and the force and torque on an element are represented as equivalent nodal forces on either side of it. We then treat the circuit as a link mechanism. Furthermore, we consider the singularity that appears in connected elements in a single circuit due to zero distance and avoid it using an approximation with a small radius. This singularity treatment makes the formula applicable even for calculation of the partial force from the entire circuit. Since the formula does not require numerical integration, it can reduce computation time. The accuracy of the approximation is also evaluated by comparing our calculations with the existing experimental results in the literature and numerical integrations.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TMAG.2018.2841382</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0003-3109-8285</orcidid><orcidid>https://orcid.org/0000-0002-0910-280X</orcidid></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | 1-D current element analytical integration Analytical models Approximation Circuits Force Lorentz covariance Lorentz force Magnetic circuits Magnetic forces Magnetism Mathematical analysis Mathematical model Mathematical models Numerical integration singularity treatment Torque |
| title | Analytical Lorentz Force Model Between 1-D Linear Currents in Arbitrary Relative Positions and Directions |
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