The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model
Abstract: It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in th… Show more
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Cited by 2 publications
References 26 publications
Existence analysis of solutions to the linear Schrödinger Kirchhoff Poisson equation based on interrupted finite elements
In this paper, we firstly explore the existence of solutions to the following linear Schrödinger Kirchhoff Poisson equation with critical exponential growth on the full space □3 by using the discontinuous finite element (DG) as well as the principle of centralized compactness: { − ( a + b ∫ □ 3 | ∇ u | 2 ) Δ u + V ( x ) u + φ u - 1 2 u Δ ( u 2 ) = K ( x ) u p − 2 u , x ∈ □ 3 − Δ φ = u 2 , x ∈ □ 3 \left\{ {\matrix{{ - \left( {a + b\int_{{\square^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + V\left( x \right)u + \phi u - {1 \over 2}u\Delta \left( {{u^2}} \right) = K\left( x \right){u^{p - 2}}u,} & {x \in {\square^3}} \cr { - \Delta \phi = {u^2},} & {x \in {\square^3}} \cr } } \right. , x ∈. Secondly, we make reasonable assumptions on the V, K , f functions of the equation, and use the principle of variational division to firstly obtain the corresponding energy generalization of this equation, and then we prove the corresponding generalizations of the equation satisfy the (C) c conditions. Finally, the existence of the solution of the equation is obtained by numerical simulation and then by using the Yamaji Lemma. The results show that the error of the finite element solution of the linear Schrödinger Kirchhoff Poisson equation in the spatial direction P1 reaches the optimal estimation under the L 2 -parameter in an intermittent finite element numerical simulation environment, i.e., it is proved that there exist at least 1 and 3 positive solutions to the problem. The paper achieves rich research results which are informative for the solution of this class of linear differential equations.
Existence analysis of solutions to the linear Schrödinger Kirchhoff Poisson equation based on interrupted finite elements
In this paper, we firstly explore the existence of solutions to the following linear Schrödinger Kirchhoff Poisson equation with critical exponential growth on the full space □3 by using the discontinuous finite element (DG) as well as the principle of centralized compactness: { − ( a + b ∫ □ 3 | ∇ u | 2 ) Δ u + V ( x ) u + φ u - 1 2 u Δ ( u 2 ) = K ( x ) u p − 2 u , x ∈ □ 3 − Δ φ = u 2 , x ∈ □ 3 \left\{ {\matrix{{ - \left( {a + b\int_{{\square^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + V\left( x \right)u + \phi u - {1 \over 2}u\Delta \left( {{u^2}} \right) = K\left( x \right){u^{p - 2}}u,} & {x \in {\square^3}} \cr { - \Delta \phi = {u^2},} & {x \in {\square^3}} \cr } } \right. , x ∈. Secondly, we make reasonable assumptions on the V, K , f functions of the equation, and use the principle of variational division to firstly obtain the corresponding energy generalization of this equation, and then we prove the corresponding generalizations of the equation satisfy the (C) c conditions. Finally, the existence of the solution of the equation is obtained by numerical simulation and then by using the Yamaji Lemma. The results show that the error of the finite element solution of the linear Schrödinger Kirchhoff Poisson equation in the spatial direction P1 reaches the optimal estimation under the L 2 -parameter in an intermittent finite element numerical simulation environment, i.e., it is proved that there exist at least 1 and 3 positive solutions to the problem. The paper achieves rich research results which are informative for the solution of this class of linear differential equations.
To better understand the research on how to improve the exercise of the college body aerobics curriculum, a method based on the equality of the half. By using the conditions in the theory of the difference between the variables to solve the selection problem in the multivariate experiment, it is equivalent to the design of the decision importance. Given the current situation of teaching aerobics in physical exercise at colleges and universities, an optimization of teaching aerobics is created. Through the test report, the relevant information has been identified. At this stage, there is no difference between the two groups in terms of skills and theoretical knowledge, but in self-exercise, the P value is less than 0.05, there is a difference, assuming that the New teaching has an important role in the development of students’ ideas. The goal is to use the best methods of teaching aerobics, solving the conflict between teaching hours and teaching methods of teaching aerobics for physical education in buildings colleges, and universities, and strive to make students get the best results in a limited time, thus making people attach importance to theoretical research and ideas of aerobics training.
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