Roman Matsyuk

Position:	Ph.D., Senior Research Associate

Affiliation:	Department of Differential Equations and Function Theory
	Institute for Applied Problems in Mechanics and Mathematics
	National Academy of Sciences of Ukraine
	and
	Lepage Research Institute, Slovakia

Address:	3-b, Naukova Str., L’viv, 790 60, Ukraine

Phone:	+38-0322-22611889

E-mail:	matsyuk-ät-lms.lviv.ua, romko.b.m-ät-gmail.com
Homepage:	iapmm.lviv.ua/12/eng/files/st_files/matsyuk/MaciukSelectedPapers.htm

Education and professional activities

Student of the Faculty of Physics, Ivan Franko L'viv State University: 1966-1971.

Postgraduate position: Institute for Applied Problems in Mechanics and Mathematics of the Academy of Science of Ukraine, L’viv (1973 up to now).

MSc. Thesis, L'viv State University, L'viv, 1971: Some generalizations of the concepts of special theory of relativity on the basis of n-point geometry, 35pp. (in Ukrainian).

PhD degree: 1985.

PhD Thesis: Poincaré-invariant equations of motion in Lagrangian mechanics with higher derivatives, 141 pp. (in Russian), Institute for Applied Problems in Mechanics and Mathematics, L'viv, 1984.

Research

Physical geometry
Differential-geometric structure of variational calculus with higher derivatives
Ostrohradskyj mechanics
Symmetries in the inverse problems of the calculus of variations

Selected Publications

Вариационный принцип для геодезических окружностей [The variational principle for geodesic circles (Russian)] corrected PDF, В кн.: Граничные задачи математической физики.– Киев: Наукова думка, 1981, с. 79–81[Boundary value problems of mathematical physics, Collect. sci. Works, Kiev 1981; Zbl 0479.35006]

О существовании лагранжиана для системы обыкновенных дифференциальных уравнений [On the existence of a Lagrangian for a system of ordinary differential equations (Russian)], „Мат. методы и физ.-мех. поля“, вып. 13.– Киев: Наукова думка, 1981, с. 34–38 [Mat. Metody i Fiz.-Mekh. Polya; MR0634648(84g:58039);Zbl 0478.34033]

Инфинитезимальные симметрии винтовых линий в плоском пространстве [Infinitesimal symmetries of helical lines in a flat space(Russian)], „Мат. методы и физ.-мех. поля“, вып. 15.– Киев: Наукова думка, 1982,с. 35–39 [Mat. Metody i Fiz.-Mekh. Polya MR0700900(84i:53005);Zbl 0486.51021]

Вариационный принцип для равноускоренного движения [Variational principle for uniformly accelerated motion (Russian PDF)], „Мат. методы и физ.-мех. поля“, вып. 16.–Киев: Наукова думка, 1982, с. 84–88 [Mat. Metody i Fiz.-Mekh. Polya; MR0700801(84g:83003); Zbl 0515.49025]

О существовании лагранжиана для неавтономной системы обыкновенных дифференциальных уравнений [Existence of a Lagrangian for a nonautonomous system of ordinary differential equations (Russian)], „Мат.методы и физ.-мех. поля“, вып. 20.–Киев: Наукова думка, 1984, с. 16–19 [Mat. Metody i Fiz.-Mekh. Polya; No. 20 (1984); MR0756973(85g:70020);Zbl 0536.34007]

Лагранжев анализ релятивистских уравнений высшего порядка траекторий частиц, геодезические окружности, равноускоренное движение и классический спин PDF, В кн.: Современные теоретические и экспериментальные проблемы теории относительности и гравитации (VI Советская гравитационная конференция).– Москва: Изд. УДН, 1984, с. 256–257.

Лагранжев анализ инвариантных уравнений движения третьего порядка в релятивистской механике классических частиц corrected PDF, English translation: Lagrangian analysis of the third-order invariant equations of motion in the relativistic mechanics of classical particles PDF, Докл. АН СССР, 1985, т. 282, №4, с. 841–844 [MR0802859(87d:70028); ISI;ISI Web; Phys. Abs., 1986, vol. 89 #93637], English translation: Sov. Phys.– Dokl. (USA), 1985, vol. 30, no. 6, 458–460 [ISI Web]

Лагранжев анализ инвариантных уравнений движения третьего порядка врелятивистской механике классических частиц corrected PDF, English translation: Lagrangian analysis of invariant third-order equations of motion in relativistic mechanics of classical particles PDF, Докл. АН СССР, 1985, т. 285, №2, с. 327–330 [MR0820861(87d:70029); ISI;ISI Web; Phys. Abs., 1987, vol. 90 #35274], English translation: Sov. Phys.– Dokl. (USA), 1985, vol. 30, no. 11, 923–925 [ISI Web]

Lagrangian approach to spinning or radiating particle higher-order equations of motion in special relativity PDF, In book: 11^th International Conference on General Relativity and Gravitation. Stockholm, Sweden, July 6–12, 1986. Abstracts of contributed papers, vol. 2.– Stockholm,1986, p. 648.

Внешние дифференциальные уравнения в обобщенной механике и свойства симметрии [Exterior differential equations in generalized mechanics and symmetry properties (Russian corrected PDF)], В кн.: Методы исследования дифференциальных и интегральных операторов.– Киев: Наук. думка, 1989, с. 153–160, 217 [Methods for studying differential and integral operators (Russian) „Naukova Dumka“, Kiev, 1989;MR1109955(92b:58009); Zbl 0719.58015]

A first order prolongation of the conventional space corrected PDF, In book: Differential Geometry and Applications. Proc. 6^th conf. DGA. Brno, August 28 – September 1 1995. – Brno: Masaryk Univ., 1996, p. 403–415 [MR1406360(97e:58061); Zbl 0867.58021]

Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrohrads'kyj mechanics PDF of corrected version, J. of Nonlinear Math. Phys, 1997, v. 4, no. 1/2, p. 89–97 [MR1401574(97h:58009); Zbl 0957.58003]

Third-order relativistic dynamics: classical spinning particle travelling in a plain. Correcter version: arXiv:1304.7494v1, Condensed Matter Physics, 1998, v. 1, no. 3(15) p. 453–462 [ISI; ISI Web]

Integration by parts and vector differential forms in higher order variational calculus on fibred manifolds PDF of corrected version, Matematychni Studii (Matematichnī Studīï), 1999, v. 11, no. 1 p. 85–107 [MR1686048(2000b:58031); Zbl 0958.58016; ISI]

Hamilton-Ostrohrads'kyj approach to relativistic free spherical top dynamics Corrected PDF, In book: Differential Geometry and Applications. Proc. 7^th conf. DGA. Brno, August 10–14 1998. – Brno: Masaryk Univ., 1999, p. 547–551 [MR1712785(2000f:70022); Zbl 0953.70016]

Лежандрівські перетворення другого ряду в механіці релятивіської дзиґи. Вісник нац. унів. „Львівська політехніка“. Прикладна математика, 2000, №411, с. 235–241

Буцім-гамільтонівський опис клясичного спіну Фізичний збірник НТШ, 2001, т. 4, с. 226–233

Autoparallel variational description of the free relativistic top third order dynamics corrected PDF, In book: Differential Geometry and Its Applications. Proc. 8^th conf. DGA. Opava, August 27–31 2001. – Opava: Silesian Univ., 2001, p. 447—459 [MR1978798(2004d:70025); Zbl 1068.70022]

A covering second-order Lagrangian for the relativistic top without forces. Improved version: arXiv:1207.3618v1, Proc. Inst. Math. of NAS of Ukraine, vol. 43 (2002), Part 2, 741–745 [MR1918395(2003f:70030); Zbl 1092.70017]

Differential geometric mechanisms in Ostrohrads'kyj relativistic spherical top dynamics, Ukrainian J. of Physics, 2003, vol. 48, №4, p. 341—349 [MR2096010(2005g:70035)

Canonical formalism for quasi-classical particle “Zitterbewegung” in Ostrohrads'kyj mechanics PDF of corrected version, In book: Differential Geometry and Its Applications. Proc. 9^th conf. DGA. Prague, August 30 – September 3 2004. – Prague: Charles University, 2005, p. 629—637 [MR2271824(2007g:70035); Zbl pre05083061]

Варіяційне узагальнення вільної релятивіської дзиґи, Фізичний збірник НТШ т. 6, 2006, с. 206–214

The next variational prolongation of the Euclidean space PDF, Tensor, 2007, vol. 68, no. 1, p. 1–9.

The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time. Corrected version: arXiv:0802.0751v2, SIGMA [Symmetry, Integrability and Geometry: Methods and Applications], 4 (2008), 016. [arXiv:0802.0751]

Variationality of geodesic circles in two dimensions PDF, In book: Differential Geometry and Its Applications. Proc. 10^th conf. DGA.Olomouc, 27-31 August 2007. – Singapore: World Scientific Publishing, 2008, – p. 635—642

Варіяційність з похідними другого порядку, релятивіське приспішення та взаємодія „дзиґи“ з тензором кривини у дво-вимірному просторі-часі, Фізичний збірник НТШ т. 7, 2008, с. 542–556

Second order variational problem and 2–dimensional concircular geometry PDF, Travaux mathématiques 2008, vol. XVIII, p. 125–137

Незмінні варіаційні рівняння третього порядку в спеціяльній теорії відносности на площині PDF виправленої версії, Прикладні проблеми механіки і математики. Вип. 7, 2009, с. 91–104.

Towards the physical significance of the (k²+A)|u| metric PDF, Tensor, 2009, vol. 71, no. 2, p. 109–113.

Higher order variational origin of the Dixon’s system and its relation to the quasi-classical ‘Zitterbewegung’ in General Relativity. Corrected version: arXiv:1101.5384v2, Differential Geometry and its Applications, 2011, vol. 29, Supplement 1,p. S149-S155

Релятивіська дзиґа в динаміці Остроградського, Фізичний збірник НТШ т. 8, 2011, с. 90–105
Relativistic mechanics of constant curvature, Journal of Mathematical Sciences, Vol. 249, No. 3, 424 – 445 (2020).

Partners & Cooperations