Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle
An alternative derivation of the equation of motion of a charged point particle from Hamilton’s principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable u i , i = 0, …, 3, being the 4-velocity. The trajectory x ¯ i ( s ) i and 4-veloci...
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| Veröffentlicht in: | Astrophysics 2015-06, Vol.58 (2), p.244-249 |
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| creator | Krikorian, R. A. |
| description | An alternative derivation of the equation of motion of a charged point particle from Hamilton’s principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable
u
i
, i = 0,
…, 3, being the 4-velocity. The trajectory
x
¯
i
(
s
)
i
and 4-velocity
ū
i
(
s
) of the particle is an optimal pair, i.e., it furnishes an extremum to the action integral. The pair
(
x
¯
,
ū)
satisfies a set of necessary conditions known as the maximum principle. Because of the path dependence of proper time s, we are concerned with a control problem with a free end point in the space of coordinates
(s
,
x
0
, …,
x
3
).
To obtain the equation of motion, the transversality condition must be satisfied at the free end point. |
| doi_str_mv | 10.1007/s10511-015-9379-4 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_hal_p</sourceid><recordid>TN_cdi_proquest_miscellaneous_1835671754</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A451633902</galeid><sourcerecordid>A451633902</sourcerecordid><originalsourceid>FETCH-LOGICAL-c540t-d1a0a570e03792e2f8ccf5d7097dd22097ba32afde9c56467ab35b502330265e3</originalsourceid><addsrcrecordid>eNqNkl-LEzEUxYMoWKsfwLcBH9SFWW-SyWTyWOquXaha_PMc0kzSZpmZdJPMot_e1NHVioLk4eaG37nkXA5CTzGcYwD-KmJgGJeAWSkoF2V1D80w47RssMD30QwYxyUnrH6IHsV4DQCiFvUM2Xc-mcIPRdqb4rUJ7lYll1tvv79c3Ix3_Vv_86aK5V6FnWmLjXdDKjcqJKc7U9jg-2KletclPzyPxSa4QbtDZx6jB1Z10Tz5Uefo8-XFp-WqXL9_c7VcrEvNKkhlixUoxsFA9kAMsY3WlrUcBG9bQnLZKkqUbY3QrK5qrraUbRkQSoHUzNA5Opvm7lUnD8H1KnyVXjm5WqylG-IogdZVJSq4xRl-McGH4G9GE5PsXdSm69Rg_BglbiirOeas-g8U44bzikJGn_2BXvsxDNl1pkiTxxHBflE71Zn8M-tTUPo4VC4qhmtKRXY1R-d_ofJpTe-0H4x1-f1E8PJEkJlkvqSdGmOUVx8_nLJ4YnXwMQZj7xaGQR5DJadQyRwqeQyVPO6BTJqY2WFnwm_m_in6BvoEyZg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1828175295</pqid></control><display><type>article</type><title>Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle</title><source>SpringerLink Journals - AutoHoldings</source><creator>Krikorian, R. A.</creator><creatorcontrib>Krikorian, R. A.</creatorcontrib><description>An alternative derivation of the equation of motion of a charged point particle from Hamilton’s principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable
u
i
, i = 0,
…, 3, being the 4-velocity. The trajectory
x
¯
i
(
s
)
i
and 4-velocity
ū
i
(
s
) of the particle is an optimal pair, i.e., it furnishes an extremum to the action integral. The pair
(
x
¯
,
ū)
satisfies a set of necessary conditions known as the maximum principle. Because of the path dependence of proper time s, we are concerned with a control problem with a free end point in the space of coordinates
(s
,
x
0
, …,
x
3
).
To obtain the equation of motion, the transversality condition must be satisfied at the free end point.</description><identifier>ISSN: 0571-7256</identifier><identifier>EISSN: 1573-8191</identifier><identifier>DOI: 10.1007/s10511-015-9379-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Astronomy ; Astrophysics ; Astrophysics and Astroparticles ; Astrophysics and Cosmology ; Bolza problems ; Derivation ; Equations of motion ; Hamilton's principle ; Hamiltonian systems ; Mathematical analysis ; Mathematical research ; Maximum principle ; Observations and Techniques ; Optimization ; Particle dynamics ; Particle physics ; Physics ; Physics and Astronomy ; Physics research ; Sciences of the Universe ; Space Exploration and Astronautics ; Space Sciences (including Extraterrestrial Physics ; Texts ; Variational principles</subject><ispartof>Astrophysics, 2015-06, Vol.58 (2), p.244-249</ispartof><rights>Springer Science+Business Media New York 2015</rights><rights>COPYRIGHT 2015 Springer</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c540t-d1a0a570e03792e2f8ccf5d7097dd22097ba32afde9c56467ab35b502330265e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10511-015-9379-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10511-015-9379-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://insu.hal.science/insu-03644940$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Krikorian, R. A.</creatorcontrib><title>Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle</title><title>Astrophysics</title><addtitle>Astrophysics</addtitle><description>An alternative derivation of the equation of motion of a charged point particle from Hamilton’s principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable
u
i
, i = 0,
…, 3, being the 4-velocity. The trajectory
x
¯
i
(
s
)
i
and 4-velocity
ū
i
(
s
) of the particle is an optimal pair, i.e., it furnishes an extremum to the action integral. The pair
(
x
¯
,
ū)
satisfies a set of necessary conditions known as the maximum principle. Because of the path dependence of proper time s, we are concerned with a control problem with a free end point in the space of coordinates
(s
,
x
0
, …,
x
3
).
To obtain the equation of motion, the transversality condition must be satisfied at the free end point.</description><subject>Astronomy</subject><subject>Astrophysics</subject><subject>Astrophysics and Astroparticles</subject><subject>Astrophysics and Cosmology</subject><subject>Bolza problems</subject><subject>Derivation</subject><subject>Equations of motion</subject><subject>Hamilton's principle</subject><subject>Hamiltonian systems</subject><subject>Mathematical analysis</subject><subject>Mathematical research</subject><subject>Maximum principle</subject><subject>Observations and Techniques</subject><subject>Optimization</subject><subject>Particle dynamics</subject><subject>Particle physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Physics research</subject><subject>Sciences of the Universe</subject><subject>Space Exploration and Astronautics</subject><subject>Space Sciences (including Extraterrestrial Physics</subject><subject>Texts</subject><subject>Variational principles</subject><issn>0571-7256</issn><issn>1573-8191</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqNkl-LEzEUxYMoWKsfwLcBH9SFWW-SyWTyWOquXaha_PMc0kzSZpmZdJPMot_e1NHVioLk4eaG37nkXA5CTzGcYwD-KmJgGJeAWSkoF2V1D80w47RssMD30QwYxyUnrH6IHsV4DQCiFvUM2Xc-mcIPRdqb4rUJ7lYll1tvv79c3Ix3_Vv_86aK5V6FnWmLjXdDKjcqJKc7U9jg-2KletclPzyPxSa4QbtDZx6jB1Z10Tz5Uefo8-XFp-WqXL9_c7VcrEvNKkhlixUoxsFA9kAMsY3WlrUcBG9bQnLZKkqUbY3QrK5qrraUbRkQSoHUzNA5Opvm7lUnD8H1KnyVXjm5WqylG-IogdZVJSq4xRl-McGH4G9GE5PsXdSm69Rg_BglbiirOeas-g8U44bzikJGn_2BXvsxDNl1pkiTxxHBflE71Zn8M-tTUPo4VC4qhmtKRXY1R-d_ofJpTe-0H4x1-f1E8PJEkJlkvqSdGmOUVx8_nLJ4YnXwMQZj7xaGQR5DJadQyRwqeQyVPO6BTJqY2WFnwm_m_in6BvoEyZg</recordid><startdate>20150601</startdate><enddate>20150601</enddate><creator>Krikorian, R. A.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope><scope>3V.</scope><scope>7TG</scope><scope>7XB</scope><scope>88I</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>KL.</scope><scope>M2P</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>Q9U</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>1XC</scope></search><sort><creationdate>20150601</creationdate><title>Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle</title><author>Krikorian, R. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c540t-d1a0a570e03792e2f8ccf5d7097dd22097ba32afde9c56467ab35b502330265e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Astronomy</topic><topic>Astrophysics</topic><topic>Astrophysics and Astroparticles</topic><topic>Astrophysics and Cosmology</topic><topic>Bolza problems</topic><topic>Derivation</topic><topic>Equations of motion</topic><topic>Hamilton's principle</topic><topic>Hamiltonian systems</topic><topic>Mathematical analysis</topic><topic>Mathematical research</topic><topic>Maximum principle</topic><topic>Observations and Techniques</topic><topic>Optimization</topic><topic>Particle dynamics</topic><topic>Particle physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Physics research</topic><topic>Sciences of the Universe</topic><topic>Space Exploration and Astronautics</topic><topic>Space Sciences (including Extraterrestrial Physics</topic><topic>Texts</topic><topic>Variational principles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Krikorian, R. A.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><collection>ProQuest Central (Corporate)</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Science Database (ProQuest)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central Basic</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Astrophysics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Krikorian, R. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle</atitle><jtitle>Astrophysics</jtitle><stitle>Astrophysics</stitle><date>2015-06-01</date><risdate>2015</risdate><volume>58</volume><issue>2</issue><spage>244</spage><epage>249</epage><pages>244-249</pages><issn>0571-7256</issn><eissn>1573-8191</eissn><abstract>An alternative derivation of the equation of motion of a charged point particle from Hamilton’s principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable
u
i
, i = 0,
…, 3, being the 4-velocity. The trajectory
x
¯
i
(
s
)
i
and 4-velocity
ū
i
(
s
) of the particle is an optimal pair, i.e., it furnishes an extremum to the action integral. The pair
(
x
¯
,
ū)
satisfies a set of necessary conditions known as the maximum principle. Because of the path dependence of proper time s, we are concerned with a control problem with a free end point in the space of coordinates
(s
,
x
0
, …,
x
3
).
To obtain the equation of motion, the transversality condition must be satisfied at the free end point.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10511-015-9379-4</doi><tpages>6</tpages></addata></record> |
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| subjects | Astronomy Astrophysics Astrophysics and Astroparticles Astrophysics and Cosmology Bolza problems Derivation Equations of motion Hamilton's principle Hamiltonian systems Mathematical analysis Mathematical research Maximum principle Observations and Techniques Optimization Particle dynamics Particle physics Physics Physics and Astronomy Physics research Sciences of the Universe Space Exploration and Astronautics Space Sciences (including Extraterrestrial Physics Texts Variational principles |
| title | Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle |
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