Geometric Mechanics and the Dynamics of Asteroid Pairs

This paper studies, using the technique of Lagrangian reduction, the geometric mechanics of a pair of asteroids in orbit about each other under mutual gravitational attraction

Desingularization of Implicit Analytic Differential Equations

The question of finding solutions to given implicit differential equations (IDE) has been answered by several authors in the last few years, using different approaches, in an algebraic and also a geometric setting. Many of those results assume in one way or another that the subimmersion theorem can be applied at several stages of the reduction algorithm, which, roughly speaking, allows to reduce a given IDE to a collection of ODE depending on parameters. The main purpose of the present paper is to improve some of the known results by introducing at each stage of the reduction algorithm a desingularization of the manifolds with singularities that may appear when the subimmersion theorem cannot be applied. This can be done for analytic IDE by using some fundamental results on subanalytic subsets and desingularization of closed subanalytic subsets due mainly to Lojasiewicz, Hironaka, Gabrielov, Hardt, Bierstone, Milman and Sussmann, among others. We will show how this approach helps to understand the dynamics given by the Lagrange-D'Alembert-Poincare equations for the symmetric elastic sphere.Comment: 50 page

Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Cocycles, compatibility, and Poisson brackets for complex fluids

Motivated by Poisson structures for complex fluids containing cocycles, such as the Poisson structure for spin glasses given by Holm and Kupershmidt in 1988, we investigate a general construction of Poisson brackets with cocycles. Connections with the construction of compatible brackets found in the theory of integrable systems are also briefly discussed

Lagrangian Reduction by Stages

This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler{Poincare reduction (for the case in which the conguration space is a Lie group) as well as Euler-Poincare reduction for semidirect products. The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange{Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory. We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange{Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory. In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of Marsden, Ratiu and Scheurle [2000], which studies the Lagrange-Routh equations

AKUNTABILITAS PENGELOLAAN ANGGARAN PENDAPATAN DAN BELANJA DESA (APBDES) 2017 DI DESA POTO

Tujuan dari penelitian ini untuk mengetahui bagaimana akuntabilitas pengelolaan pendapatan dan belanja di desa Poto yang meliputi kegiatan perencanaan, pelaksanaan, penatausaaan, penatausahaan dan pertanggungjawaban yang digunakan metode kualitatif dengan pendekatan deskritif kualitatif. Hasil penelitian ini menujukan bahwa Akuntabilitas di Desa Poto Kec. Moyo Hilir Kab. Sumbawa secara umum sudah baik. Hanya saja ada beberapa tahap yang tidak sesuai dengan peraturan menteri dalam negeri No.2014. untuk tahap perencanaan Sekretaris Desa menyampaikan rancangan Peraturan Desa tenang APBDes berdasarkan RKPDes kepada Kepala Desa. Kemudian dibahas dan disepakati Kepala Desa dan Badan Permusyawaratan Desa. Hal ini telah sesuai dengan Permendagri No.113 . untuk tahap pelaksanaan semua penerimaan dan pengeluaran dalam rangka pelaksanaan kewenangan desa dilaksanakan melalui rekening kas desa dan Pemerintah desa dilarang melakukan pungutan sebagai penerimaan desa Hal ini telah sesuai dengan Permendagri No.113 .dan tahap pertanggungjawaban Hasil yang diperoleh dari lapangan pertanggungjawaban keuangan Desa Poto, dimana dalam hal ini terjadi sedikit ketidaaksesuaian yaitu pertanggungjawaban belum diinformasikan secara maksimal kepada seluruh masyarakat Desa Poto, berdasarkan Permendagri No.113 Tahun 2014 pasal 40 yang mengatur bahwa laporan pertanggungjawaban realisasi pelaksanaan APBDes diinformasikan kepada masyarakat secara tertulis dan dengan media yang mudah diakses oleh masyarakat karen

Perancangan Aplikasi Pengolahan Data Logistik pada Kantor Cabang Bri Solok

With the development of information technology companies are required to improve the efficiency and quality of service. The logistics department not only serves to support the office operations but one of the functions that will improve the effectiveness and efficiency of the company. This research was conducted to assist the logistics department in making efficient use of time, energy and cost in making logistic report at Bank Rakyat Indonesia branch of Solok. In this research will be made data processing logistics system using Java programming language and MySQL database. Based on data obtained by way of observation and interview further data analyzed to make system design as needed. Keywords : Data Processing Logistics, JAVA, MYSQ

Kompetensi Sikap Mahasiswa Calon Guru Di Universitas Islam Riau

Penelitian ini bertujuan untuk mendeskripsikan kompetensi sikap mahasiswa calon guru di Universitas Islam Riau angkatan 2017/2018. Jenis penelitian deskriptif kuantitatif. Lokasi penelitian dilaksanakan di FKIP Universitas Islam Riau. Sedangkan yang menjadi subjek penelitian adalah mahasiswa calon guru FKIP Univeristas Islam Riau yang berjumlah 100 orang dengan teknik pengambilan sampel cluster random sampling. Tahapan penelitian dilakukan dengan tiga tahap, yaitu: 1) pra lapangan; 2) pekerjaan lapangan; dan 3) analisis data. Teknik pengumpulan data menggunakan angket skala sikap. Metode analisis data yang digunakan adalah statistik deskriptif, statistik ini ditujukan untuk mengumpulkan data, menyajikan data dan menentukan nilai. Hasil penelitian dituangkan dalam 4 kategori yaitu baik sekali, baik, cukup, dan kurang. Berdasarkan analisis data yang telah dilakukan maka dapat disimpulkan penelitian ini yaitu kompetensi sikap calon guru mahasiswa Fakultas Keguruan dan Ilmu Pendidikan Universitas Islam Riau termasuk kategori baik dengan persentase sebesar 53% dari total sampel. Hal ini membuktikan bahwa mahasiswa calon guru FKIP UIR memiliki kompetensi sikap yang baik untuk menjadi calon guru