3 research outputs found
ΠΠ΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½Π΅ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ ΡΠΎΡΠΌΠΈ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Ρ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ ΠΏΡΠ΄ Π²ΠΏΠ»ΠΈΠ²ΠΎΠΌ ΡΠΌΠΏΡΠ»ΡΡΡΠ² Π½Π° ΠΊΡΠ½ΡΠ΅Π²Ρ ΡΠΎΡΠΊΠΈ ΡΡ Π»Π°Π½ΠΎΠΊ
We have examined a geometrical model of the new technique for unfolding a multilink rod structure under conditions of weightlessness. Displacement of elements of the links occurs due to the action of pulses from pyrotechnic jet engines to the end points of links in a structure. A description of the dynamics of the obtained inertial unfolding of a rod structure is performed using the Lagrange equation of second kind, built using the kinetic energy of an oscillatory system only.The relevance of the chosen subject is indicated by the need to choose and explore a possible engine of the process of unfolding a rod structure of the pendulum type. It is proposed to use pulse pyrotechnic jet engines installed at the end points of links in a rod structure. They are lighter and cheaper as compared, for example, with electric motors or spring devices. This is economically feasible when the process of unfolding a structure in orbit is scheduled to run only once.We have analyzed manifestations of possible errors in the magnitudes of pulses on the geometrical shape of the arrangement of links in a rod structure, acquired as a result of its unfolding. It is shown at the graphical level that the error may vary within one percent of the estimated value of the magnitude of a pulse. To determine the moment of fixing the elements of a multilink structure in the preset unfolded state, it is proposed to use a Β«stop-codeΒ». It is a series of numbers, which, by using functions of the generalized coordinates of the Lagrange equation of second kind, define the current values of angles between the elements of a rod structure.Results are intended for geometrical modeling of the unfolding of large-size structures under conditions of weightlessness, for example, power frames for solar mirrors, or cosmic antennae, as well as other large-scale orbital facilities.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Π° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ Π½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΏΠΎΡΠΎΠ±Π° ΡΠ°ΡΠΊΡΡΡΠΈΡ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ, ΡΠ»Π΅ΠΌΠ΅Π½ΡΡ ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½Ρ ΠΏΠΎΠ΄ΠΎΠ±Π½ΠΎ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΌΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΡ. Π Π°ΡΠΊΡΡΡΠΈΠ΅ Π·Π²Π΅Π½ΡΠ΅Π² ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π±Π»Π°Π³ΠΎΠ΄Π°ΡΡ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ² ΠΏΠΈΡΠΎΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΡΡ
Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Π΅ΠΉ Π½Π° ΠΊΠΎΠ½Π΅ΡΠ½ΡΠ΅ ΡΠΎΡΠΊΠΈ ΠΈΡ
Π·Π²Π΅Π½ΡΠ΅Π². ΠΠΏΠΈΡΠ°Π½ΠΈΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½Π΅ΡΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΊΡΡΡΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΎ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π²ΡΠΎΡΠΎΠ³ΠΎ ΡΠΎΠ΄Π°. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ΅Π½Ρ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠΈΡΡΠ΅ΠΌ ΡΠ°ΡΠΊΡΡΡΠΈΡ ΠΊΡΡΠΏΠ½ΠΎΠ³Π°Π±Π°ΡΠΈΡΠ½ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΡΡΠΈ, Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ, ΡΠΈΠ»ΠΎΠ²ΡΡ
ΠΊΠ°ΡΠΊΠ°ΡΠΎΠ² Π΄Π»Ρ ΡΠΎΠ»Π½Π΅ΡΠ½ΡΡ
Π·Π΅ΡΠΊΠ°Π» ΠΈΠ»ΠΈ ΠΊΠΎΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π½ΡΠ΅Π½Π½ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½Π° ΠΌΠΎΠ΄Π΅Π»Ρ Π½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΏΠΎΡΠΎΠ±Ρ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π² ΡΠΌΠΎΠ²Π°Ρ
Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ, Π΅Π»Π΅ΠΌΠ΅Π½ΡΠΈ ΡΠΊΠΎΡ Π·βΡΠ΄Π½Π°Π½Ρ ΠΏΠΎΠ΄ΡΠ±Π½ΠΎ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΠΌΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΡ. Π ΠΎΠ·ΠΊΡΠΈΡΡΡ Π»Π°Π½ΠΎΠΊ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ Π·Π°Π²Π΄ΡΠΊΠΈ Π²ΠΏΠ»ΠΈΠ²Ρ ΡΠΌΠΏΡΠ»ΡΡΡΠ² ΠΏΡΡΠΎΡΠ΅Ρ
Π½ΡΡΠ½ΠΈΡ
ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΠΈΡ
Π΄Π²ΠΈΠ³ΡΠ½ΡΠ² Π½Π° ΡΡ
ΠΊΡΠ½ΡΠ΅Π²Ρ ΡΠΎΡΠΊΠΈ. ΠΠΏΠΈΡ Π΄ΠΈΠ½Π°ΠΌΡΠΊΠΈ ΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΎΠ³ΠΎ ΡΠ½Π΅ΡΡΡΠΉΠ½ΠΎΠ³ΠΎ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π²ΠΈΠΊΠΎΠ½Π°Π½ΠΎ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ ΡΡΠ²Π½ΡΠ½Π½Ρ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π΄ΡΡΠ³ΠΎΠ³ΠΎ ΡΠΎΠ΄Ρ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΡΠΈΠ·Π½Π°ΡΠ΅Π½ΠΎ Π΄Π»Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΡΠ²Π°Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π²Π΅Π»ΠΈΠΊΠΎΠ³Π°Π±Π°ΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ Π² ΡΠΌΠΎΠ²Π°Ρ
Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ, Π½Π°ΠΏΡΠΈΠΊΠ»Π°Π΄, ΡΠΈΠ»ΠΎΠ²ΠΈΡ
ΠΊΠ°ΡΠΊΠ°ΡΡΠ² Π΄Π»Ρ ΡΠΎΠ½ΡΡΠ½ΠΈΡ
Π΄Π·Π΅ΡΠΊΠ°Π» ΡΠΈ ΠΊΠΎΡΠΌΡΡΠ½ΠΈΡ
Π°Π½ΡΠ΅
ΠΠ΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½Π΅ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ ΡΠΎΡΠΌΠΈ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Ρ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ ΠΏΡΠ΄ Π²ΠΏΠ»ΠΈΠ²ΠΎΠΌ ΡΠΌΠΏΡΠ»ΡΡΡΠ² Π½Π° ΠΊΡΠ½ΡΠ΅Π²Ρ ΡΠΎΡΠΊΠΈ ΡΡ Π»Π°Π½ΠΎΠΊ
We have examined a geometrical model of the new technique for unfolding a multilink rod structure under conditions of weightlessness. Displacement of elements of the links occurs due to the action of pulses from pyrotechnic jet engines to the end points of links in a structure. A description of the dynamics of the obtained inertial unfolding of a rod structure is performed using the Lagrange equation of second kind, built using the kinetic energy of an oscillatory system only.The relevance of the chosen subject is indicated by the need to choose and explore a possible engine of the process of unfolding a rod structure of the pendulum type. It is proposed to use pulse pyrotechnic jet engines installed at the end points of links in a rod structure. They are lighter and cheaper as compared, for example, with electric motors or spring devices. This is economically feasible when the process of unfolding a structure in orbit is scheduled to run only once.We have analyzed manifestations of possible errors in the magnitudes of pulses on the geometrical shape of the arrangement of links in a rod structure, acquired as a result of its unfolding. It is shown at the graphical level that the error may vary within one percent of the estimated value of the magnitude of a pulse. To determine the moment of fixing the elements of a multilink structure in the preset unfolded state, it is proposed to use a Β«stop-codeΒ». It is a series of numbers, which, by using functions of the generalized coordinates of the Lagrange equation of second kind, define the current values of angles between the elements of a rod structure.Results are intended for geometrical modeling of the unfolding of large-size structures under conditions of weightlessness, for example, power frames for solar mirrors, or cosmic antennae, as well as other large-scale orbital facilities.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Π° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ Π½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΏΠΎΡΠΎΠ±Π° ΡΠ°ΡΠΊΡΡΡΠΈΡ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΡΡΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ, ΡΠ»Π΅ΠΌΠ΅Π½ΡΡ ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½Ρ ΠΏΠΎΠ΄ΠΎΠ±Π½ΠΎ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΌΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΡ. Π Π°ΡΠΊΡΡΡΠΈΠ΅ Π·Π²Π΅Π½ΡΠ΅Π² ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π±Π»Π°Π³ΠΎΠ΄Π°ΡΡ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΈΠΌΠΏΡΠ»ΡΡΠΎΠ² ΠΏΠΈΡΠΎΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΡΡ
Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Π΅ΠΉ Π½Π° ΠΊΠΎΠ½Π΅ΡΠ½ΡΠ΅ ΡΠΎΡΠΊΠΈ ΠΈΡ
Π·Π²Π΅Π½ΡΠ΅Π². ΠΠΏΠΈΡΠ°Π½ΠΈΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½Π΅ΡΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΊΡΡΡΠΈΡ ΠΌΠ½ΠΎΠ³ΠΎΠ·Π²Π΅Π½Π½ΠΎΠΉ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΎ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π²ΡΠΎΡΠΎΠ³ΠΎ ΡΠΎΠ΄Π°. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ΅Π½Ρ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠΈΡΡΠ΅ΠΌ ΡΠ°ΡΠΊΡΡΡΠΈΡ ΠΊΡΡΠΏΠ½ΠΎΠ³Π°Π±Π°ΡΠΈΡΠ½ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΡΡΠΈ, Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ, ΡΠΈΠ»ΠΎΠ²ΡΡ
ΠΊΠ°ΡΠΊΠ°ΡΠΎΠ² Π΄Π»Ρ ΡΠΎΠ»Π½Π΅ΡΠ½ΡΡ
Π·Π΅ΡΠΊΠ°Π» ΠΈΠ»ΠΈ ΠΊΠΎΡΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π½ΡΠ΅Π½Π½ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π° Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½Π° ΠΌΠΎΠ΄Π΅Π»Ρ Π½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΏΠΎΡΠΎΠ±Ρ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π² ΡΠΌΠΎΠ²Π°Ρ
Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ, Π΅Π»Π΅ΠΌΠ΅Π½ΡΠΈ ΡΠΊΠΎΡ Π·βΡΠ΄Π½Π°Π½Ρ ΠΏΠΎΠ΄ΡΠ±Π½ΠΎ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΠΌΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΡ. Π ΠΎΠ·ΠΊΡΠΈΡΡΡ Π»Π°Π½ΠΎΠΊ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ Π·Π°Π²Π΄ΡΠΊΠΈ Π²ΠΏΠ»ΠΈΠ²Ρ ΡΠΌΠΏΡΠ»ΡΡΡΠ² ΠΏΡΡΠΎΡΠ΅Ρ
Π½ΡΡΠ½ΠΈΡ
ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΠΈΡ
Π΄Π²ΠΈΠ³ΡΠ½ΡΠ² Π½Π° ΡΡ
ΠΊΡΠ½ΡΠ΅Π²Ρ ΡΠΎΡΠΊΠΈ. ΠΠΏΠΈΡ Π΄ΠΈΠ½Π°ΠΌΡΠΊΠΈ ΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΎΠ³ΠΎ ΡΠ½Π΅ΡΡΡΠΉΠ½ΠΎΠ³ΠΎ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π±Π°Π³Π°ΡΠΎΠ»Π°Π½ΠΊΠΎΠ²ΠΎΡ ΡΡΠ΅ΡΠΆΠ½Π΅Π²ΠΎΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΡ Π²ΠΈΠΊΠΎΠ½Π°Π½ΠΎ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ ΡΡΠ²Π½ΡΠ½Π½Ρ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π΄ΡΡΠ³ΠΎΠ³ΠΎ ΡΠΎΠ΄Ρ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΡΠΈΠ·Π½Π°ΡΠ΅Π½ΠΎ Π΄Π»Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΏΡΠΈ ΠΏΡΠΎΠ΅ΠΊΡΡΠ²Π°Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌ ΡΠΎΠ·ΠΊΡΠΈΡΡΡ Π²Π΅Π»ΠΈΠΊΠΎΠ³Π°Π±Π°ΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ Π² ΡΠΌΠΎΠ²Π°Ρ
Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡΡΡ, Π½Π°ΠΏΡΠΈΠΊΠ»Π°Π΄, ΡΠΈΠ»ΠΎΠ²ΠΈΡ
ΠΊΠ°ΡΠΊΠ°ΡΡΠ² Π΄Π»Ρ ΡΠΎΠ½ΡΡΠ½ΠΈΡ
Π΄Π·Π΅ΡΠΊΠ°Π» ΡΠΈ ΠΊΠΎΡΠΌΡΡΠ½ΠΈΡ
Π°Π½ΡΠ΅