Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints
Апстракт
The paper analyzes the problem of brachistochronic motion of a nonholonomic
mechanical system, using an example of a simple car model. The system moves between
two default positions at an unaltered value of the mechanical energy during motion.
Differential equations of motion, containing the reaction of nonholonomic constraints and
control forces, are obtained on the basis of general theorems of dynamics. Here, this is more
appropriate than some other methods of analytical mechanics applied to nonholonomic
systems, where the provision of a subsequent physical interpretation of the multipliers of
constraints is required to solve this problem. By the appropriate choice of the parameters of
state as simple a task of optimal control as possible is obtained in this case, which is solved
by the application of the Pontryagin maximum principle. Numerical solution of the twopoint
boundary value problem is obtained by the method of shooting. Based on the thus
acquired brachistochronic... motion, the active control forces are determined as well as the
reaction of constraints. Using the Coulomb laws of friction sliding, the minimum value of
the coefficient of friction is determined to avoid car skidding at the points of contact with
the ground.
Извор:
Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013, 2013, 903-908Издавач:
- Beograd : Srpsko društvo za mehaniku
Финансирање / пројекти:
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Radulović, Radoslav AU - Obradović, Aleksandar AU - Jeremić, Bojan PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4038 AB - The paper analyzes the problem of brachistochronic motion of a nonholonomic mechanical system, using an example of a simple car model. The system moves between two default positions at an unaltered value of the mechanical energy during motion. Differential equations of motion, containing the reaction of nonholonomic constraints and control forces, are obtained on the basis of general theorems of dynamics. Here, this is more appropriate than some other methods of analytical mechanics applied to nonholonomic systems, where the provision of a subsequent physical interpretation of the multipliers of constraints is required to solve this problem. By the appropriate choice of the parameters of state as simple a task of optimal control as possible is obtained in this case, which is solved by the application of the Pontryagin maximum principle. Numerical solution of the twopoint boundary value problem is obtained by the method of shooting. Based on the thus acquired brachistochronic motion, the active control forces are determined as well as the reaction of constraints. Using the Coulomb laws of friction sliding, the minimum value of the coefficient of friction is determined to avoid car skidding at the points of contact with the ground. PB - Beograd : Srpsko društvo za mehaniku C3 - Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013 T1 - Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints EP - 908 SP - 903 UR - https://hdl.handle.net/21.15107/rcub_machinery_4038 ER -
@conference{ author = "Radulović, Radoslav and Obradović, Aleksandar and Jeremić, Bojan", year = "2013", abstract = "The paper analyzes the problem of brachistochronic motion of a nonholonomic mechanical system, using an example of a simple car model. The system moves between two default positions at an unaltered value of the mechanical energy during motion. Differential equations of motion, containing the reaction of nonholonomic constraints and control forces, are obtained on the basis of general theorems of dynamics. Here, this is more appropriate than some other methods of analytical mechanics applied to nonholonomic systems, where the provision of a subsequent physical interpretation of the multipliers of constraints is required to solve this problem. By the appropriate choice of the parameters of state as simple a task of optimal control as possible is obtained in this case, which is solved by the application of the Pontryagin maximum principle. Numerical solution of the twopoint boundary value problem is obtained by the method of shooting. Based on the thus acquired brachistochronic motion, the active control forces are determined as well as the reaction of constraints. Using the Coulomb laws of friction sliding, the minimum value of the coefficient of friction is determined to avoid car skidding at the points of contact with the ground.", publisher = "Beograd : Srpsko društvo za mehaniku", journal = "Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013", title = "Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints", pages = "908-903", url = "https://hdl.handle.net/21.15107/rcub_machinery_4038" }
Radulović, R., Obradović, A.,& Jeremić, B.. (2013). Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints. in Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013 Beograd : Srpsko društvo za mehaniku., 903-908. https://hdl.handle.net/21.15107/rcub_machinery_4038
Radulović R, Obradović A, Jeremić B. Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints. in Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013. 2013;:903-908. https://hdl.handle.net/21.15107/rcub_machinery_4038 .
Radulović, Radoslav, Obradović, Aleksandar, Jeremić, Bojan, "Brachistohronic motion of a nonholonomic mechanical system with limited reaction of constraints" in Proceeding of Fourth Serbian (29th Yu) Congress on Theoretical and Applied Mechanics Vrnja ka Banja, Serbia, 4-7 June 2013 (2013):903-908, https://hdl.handle.net/21.15107/rcub_machinery_4038 .