summary:In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred... more summary:In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example
summary:In this paper we derive general equations for constraint Noethertype symmetries of a firs... more summary:In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory and the equations of symmetries and conservation laws derived within this framework we present the Chaplygin sleigh. It is a mechanical system subject to one linear nonholonomic constraint enforcing the plane motion. We describe the trajectories of the Chaplygin sleigh and show that the usual kinetic energy conservation law holds along them, the time translation generator being the corresponding constraint symmetry and simultaneously the symmetry of nonholonomic equations of motion....
The Chaplygin sleigh is a mechanical system subject to one linear nonholonomic constraint enforci... more The Chaplygin sleigh is a mechanical system subject to one linear nonholonomic constraint enforcing the plane motion. We solve equations of motion and study symmetries and conservation laws for this system after deriving general equations of nonholonomic symmetries of the constraint Lagrangian. Our considerations are based on an efficient geometrical theory on fibred manifolds first presented and developed by Olga Rossi (Krupkova). The obtained results are thoroughly discussed from the point of view of physics.
As widely accepted, justified by the historical developments of physics, the background for stand... more As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \true trajectories" of the physical systems represent stationary points of the corresponding functionals. It turns out that equations of motion in most of the fundamental theories of physics (as e.g. classical mechanics, mechanics of continuous media or fluids, electrodynamics, quantum mechanics, string theory, etc.), are Euler-L...
Přispěvek pojednava o problematice přesneho měřeni mřižkových parametrů kubických a dvouparametro... more Přispěvek pojednava o problematice přesneho měřeni mřižkových parametrů kubických a dvouparametrových krystalických latek z rentgenogramů ziskaných praskovou Debyeovou-Scherrerovou metodou pomoci nomogramů M. Cernohorskeho a podilovou metodou v obdobi 1960 a později. Ukazuje, že těmito metodami se v době bez pocitaců dosahovalo vysoke přesnosti několika desetitisicin procenta, tedy o řad lepsi, než dosahovaly tehdejsi předni světove laboratoře.
V osobni vzpomince [1] na profesora Masarykovy univerzity, významneho teoretickeho fyzika a matem... more V osobni vzpomince [1] na profesora Masarykovy univerzity, významneho teoretickeho fyzika a matematika Bohuslava Hostinskeho naznacil jeji autor Cestmir Simaně, mj. s odkazem na Nelsonovu praci [5], možnost, že prof. Hostinský, aniž sam byl přiznivcem kvantove fyziky, mohl na zakladě svých vlastnich výzkumů v oblasti mechanických kmitů intuitivně směřovat k některým jejim výsledkům. Můžeme zjistit, zda tomu tak opravdu bylo, nebo zda to je alespoň pravděpodobne? Tento přispěvek, přednesený tež na seminaři pořadanem letos k poctě Bohuslava Hostinskeho na Masarykově univerzitě v Brně [2], se pokousi najit možne souvislosti a odpovědi.
Informace o uspěchu soutěžni prace studenta gymnazia vedene pracovniky Ustavu teoreticke fyziky a... more Informace o uspěchu soutěžni prace studenta gymnazia vedene pracovniky Ustavu teoreticke fyziky a astrofyziky Přirodovědecke fakulty MU. Fyzikalni charakteristika prace zabývajici se modely valiveho odporu a charakteristika originalnich výsledků ziskaných v ramci prace.
summary:In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred... more summary:In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example
summary:In this paper we derive general equations for constraint Noethertype symmetries of a firs... more summary:In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory and the equations of symmetries and conservation laws derived within this framework we present the Chaplygin sleigh. It is a mechanical system subject to one linear nonholonomic constraint enforcing the plane motion. We describe the trajectories of the Chaplygin sleigh and show that the usual kinetic energy conservation law holds along them, the time translation generator being the corresponding constraint symmetry and simultaneously the symmetry of nonholonomic equations of motion....
The Chaplygin sleigh is a mechanical system subject to one linear nonholonomic constraint enforci... more The Chaplygin sleigh is a mechanical system subject to one linear nonholonomic constraint enforcing the plane motion. We solve equations of motion and study symmetries and conservation laws for this system after deriving general equations of nonholonomic symmetries of the constraint Lagrangian. Our considerations are based on an efficient geometrical theory on fibred manifolds first presented and developed by Olga Rossi (Krupkova). The obtained results are thoroughly discussed from the point of view of physics.
As widely accepted, justified by the historical developments of physics, the background for stand... more As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \true trajectories" of the physical systems represent stationary points of the corresponding functionals. It turns out that equations of motion in most of the fundamental theories of physics (as e.g. classical mechanics, mechanics of continuous media or fluids, electrodynamics, quantum mechanics, string theory, etc.), are Euler-L...
Přispěvek pojednava o problematice přesneho měřeni mřižkových parametrů kubických a dvouparametro... more Přispěvek pojednava o problematice přesneho měřeni mřižkových parametrů kubických a dvouparametrových krystalických latek z rentgenogramů ziskaných praskovou Debyeovou-Scherrerovou metodou pomoci nomogramů M. Cernohorskeho a podilovou metodou v obdobi 1960 a později. Ukazuje, že těmito metodami se v době bez pocitaců dosahovalo vysoke přesnosti několika desetitisicin procenta, tedy o řad lepsi, než dosahovaly tehdejsi předni světove laboratoře.
V osobni vzpomince [1] na profesora Masarykovy univerzity, významneho teoretickeho fyzika a matem... more V osobni vzpomince [1] na profesora Masarykovy univerzity, významneho teoretickeho fyzika a matematika Bohuslava Hostinskeho naznacil jeji autor Cestmir Simaně, mj. s odkazem na Nelsonovu praci [5], možnost, že prof. Hostinský, aniž sam byl přiznivcem kvantove fyziky, mohl na zakladě svých vlastnich výzkumů v oblasti mechanických kmitů intuitivně směřovat k některým jejim výsledkům. Můžeme zjistit, zda tomu tak opravdu bylo, nebo zda to je alespoň pravděpodobne? Tento přispěvek, přednesený tež na seminaři pořadanem letos k poctě Bohuslava Hostinskeho na Masarykově univerzitě v Brně [2], se pokousi najit možne souvislosti a odpovědi.
Informace o uspěchu soutěžni prace studenta gymnazia vedene pracovniky Ustavu teoreticke fyziky a... more Informace o uspěchu soutěžni prace studenta gymnazia vedene pracovniky Ustavu teoreticke fyziky a astrofyziky Přirodovědecke fakulty MU. Fyzikalni charakteristika prace zabývajici se modely valiveho odporu a charakteristika originalnich výsledků ziskaných v ramci prace.
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