scholarly journals VIII. On the theory of the moon

1834 ◽  
Vol 124 ◽  
pp. 127-141
Keyword(s):  
Differential Equations ◽  
Great Increase ◽  
Direct Method ◽  
Sufficient Accuracy ◽  
The Moon ◽  
Great Precision ◽  
Similar Series ◽  
Independent Variable ◽  
The Subject ◽  
The Mean

When I commenced the investigations relating to the theory of the moon which I have had the honour to communicate to the Society, I proposed to show how, by a different but more direct method, the numerical results given by M. Damoiseau might be obtained. The approximations were in fact carried much further by M. Damoiseau than had been done before, and the details which accompany M. Damoiseau's work evince at once the immense labour of the undertaking, and inspire confidence in the accuracy of the results offered. But the state of the question is now changed by the appearance of M. Plana’s admirable work, entitled “Théorie du Mouvement de la Lune,” in which, although M. Plana's employs the same differential equations as those used by M. Damoiseau, and obtains in the same manner finally the expressions for the coordinates of the moon, in terms of the mean longitude by the reversion of series, yet M. Plana’s expressions have a very different analytical character and im­portance, from the circumstance that the author develops all the quantities intro­duced by integration, according to powers of the quantity called m , which expresses the ratio of the sun’s mean motion to that of the moon. In this form of the expression the coefficients of the different powers of m , of the eccentricity, &c., are determinate, as are, for example, the numerical coefficients in the expression for the sine in terms of the arc, and other similar series. An inestimable advantage results from this pro­cedure, which more than compensates for the great increase of labour it occasions, by diminishing the danger of neglecting any terms of the same order as those taken into account, and by affording the means of verifying many terms long before final and complete results shall have been obtained independently by myself or any other person. By treating the differential equations in which the time is the independent variable, as I have proposed, similar results to those of M. Plana may be obtained directly; but the calculations which are required in either method are so prodigiously irksome and laborious, that until identical expressions have actually been obtained independently, to the extent of every sensible term, the theory of the moon cannot, I think, be considered complete. It might, indeed, be supposed that already, through the labours of mathematicians, from Clairaut to the present time, the numerical values of the coefficients of the different inequalities were ascertained with sufficient accuracy for practical purposes, and that any further researches connected with the subject would be more likely to gratify curiosity than to lead to any useful result. Astronomical observations are now made with so great precision, that the numerical values of the coefficients are wanted to at least the tenth of a second of space: very few, however, of the coefficients of MM. Damoiseau and Plana agree so nearly, and some differ much more, as may be seen in the following comparison of the numerical values of the coefficients of some of the arguments in the expression for the true longitude of the moon in terms of her mean longitude, being indeed those which differ the most.

XV. — Researches in physical astronomy

1831 ◽  
Vol 121 ◽  
pp. 231-282
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Lunar Theory ◽  
System Of Equations ◽  
Planetary Theory ◽  
The Moon ◽  
Celestial Bodies ◽  
Independent Variable ◽  
The Mean ◽  
The One

The method pursued by Clairaut in the solution of this important problem of Physical Astronomy, consists in the integration of the differential equations furnished by the principles of dynamics, upon the hypothesis that in the gravitation of the celestial bodies the force varies inversely as the square of the distance, and in which the true longitude of the moon is the independent variable ; the time is thus obtained in terms of the true longitude, and by the reversion of series the longitude is afterwards obtained in terms of the time, which is necessary for the purpose of forming astronomical tables. But while on the one hand this method possesses the advantage, that the disturbing func­tion can be developed with somewhat greater facility in terms of the true lon­gitude of the moon than in terms of the mean longitude, yet on the other hand, the differential equations in which the true longitude is the independent variable are far more complicated than those in which the time is the inde­pendent variable. The latter equations are used in the planetary theory ; so that the method of Clairaut has the additional inconvenience, that while the lunar theory is a particular case of the problem of the three bodies, one system of equations is used in this case, and another in the case of the planets. The method of Clairaut has been adopted, however, by Mayer, by Laplace, and by M. Damoiseau. The last-mentioned author has arranged his results with remarkable clearness, so that any part of his processes may be easily verified by any one who does not shrink from this gigantic undertaking; and the immense labour which this method requires, when all sensible quantities are retained, may be seen in his invaluable memoir. Mr. Brice Bronwin has recently communicated to the Society a lunar theory, in which the same method is adopted.

scholarly journals Penerapan Konsep Persamaan Diferensial Biasa Pada Pemodelan Tali Penahan Jembatan Gantung

2021 ◽  
Vol 1 (4) ◽  
pp. 559-569
Author(s):  
Sri Wulandari Pratiwi ◽  
Arjudin Arjudin ◽  
Nani Kurniati ◽  
Sripatmi Sripatmi
Keyword(s):  
Data Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Quantitative Research ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
First Order ◽  
Independent Variable ◽  
The Subject ◽  
Development Methods

bridge from the concept of ordinary differential equations and to determine solving differential equations and capitalizing suspension bridges, with the suspension bridge in Gerung, West Lombok is a modeling. The type of this research is Quantitative research with development methods literature. The subject in this research retaining ropes on suspension bridges. The data collected in the form of journals or articles from various related sources model of the retaining rope on a computed suspension bridge analyzed and concluded by the researcher through data analysis techniques by using the type of research triangulation principle and theoretical triangulation based on the results of data analysis, it was found that differential equations can be applied to modeling suspension bridges through first-order ordinary differential equations with the form of capitalization equations with the solution , with the interval in . The Gerung suspension bridge has its retaining rope modeling solution is , in 12 right suspensions at each hose in the interval the related variable is the height of the retaining rope and x the independent variable is the distance from the lowest restraint to the rope to be measured.

scholarly journals HUBUNGAN ANTARA KONSEP DIRI DENGAN KOMUNIKASI INTERPERSONAL PADA ANGGOTA SATUAN LALULINTAS (SATLANTAS) POLRES BANTUL

2017 ◽  
Vol 3 (2) ◽  
pp. 19
Author(s):  
Suprastowo Damarhadi ◽  
Berliana Henu Cahyani
Keyword(s):  
Interpersonal Communication ◽  
Random Sampling ◽  
The Self ◽  
Self Concept ◽  
Interpersonal Communications ◽  
Communication Variable ◽  
Independent Variable ◽  
The Subject ◽  
The Mean ◽  
The Relationship

ABSTRACTThe aim of this research are want to know about the relationship between self concept and police’s interpersonal communications at Polres Bantul, and want to know the effective support fron the self concept to police’s interpersonal communications at Polres Bantul.There are two variables in this research. The independent variable is police’s interpersonal communications and the dependent variable is self concept. The subject’s characteristic are (1) the police at Polres Bantu; (2) man or woman; (3) have 2 years minimal eksperient work at Bantul. The population are 157 police. Random sampling use as a technic to choose the subject. There are two scale in this research, communication interpersonal scale and self concept scale. The method for analysis is the correlations of product moment.The conclusion there are the relationship between self concept and police’s interpersonal communications. The higher self concept will make the communication interpersonal be higher too. The hypothesis can accept, it’s the mean there are the relationship between self concept and police’s interpersonal communications. The effective score for self concept to interpersonal communication 25,8%. It’s the mean 74,2% interpersonal communication variable is support another variable for examples are perception and memory. Key Words: Interpersonal Communication, Self Concept

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 51-52
Keyword(s):  
Differential Equations ◽  
Great Distance ◽  
Original Position ◽  
Lunar Theory ◽  
Great Length ◽  
The Moon ◽  
The Earth ◽  
Method Of Solution ◽  
Independent Variable ◽  
The One

The first part of this paper relates to the theory of the moon. The method of solution pursued by Clairaut consisted in the inte­gration of differential equations, in which the true longitude of the moon is the independent variable: the time is then obtained in terms of the true longitude; and by the reversion of series, the lon­gitude afterwards obtained in terms of the time. This method is the one adopted by Mayer, Laplace, and Damoiseau. The au­thor has been led, by reflecting on the difficulties of this problem, to believe that the integration of the differential equations in which the time is the independent variable would be at least as easy as the former process; and it would possess the advantage of employing the same system of equations for the moon as for the planets. The lunar theory proposed by the author, and developed in this paper, is an extension of the equations given in his former Researches in Physical Astronomy, already published in the Philosophical Trans­actions; by including those terms, which, in consequence of the great eccentricity of the moon’s orbit, are sensible; and by sup­pressing those which are insensible from the great distance of the sun, the disturbing body. He has not yet attempted to obtain numerical results, but proposes at some future time to engage in their computation. In the second part of the paper, he investigates the precession of the equinoxes, on the supposition that the earth revolves in a re­sisting medium; an investigation which may also be considered as a sequel to the author’s last paper on Physical Astronomy. The effects of the resistance of such a medium is to increase the latitude of the axis of rotation (reckoned from the equator of the figure) till it reaches 90°. Such is now the condition of the axis of the earth: but as the chances are infinitely great against this having been its original position, may not its attainment of this position be ascribed to the resistance of a medium of small density acting for a great length of time, —a supposition which may account for many geological indications of changes having taken place in the climates of the earth ? The operation of such a cause would be also sen­sible in the case of comets: and the accuracy with which the ec­centricity of the Halleian comet of 1759 is known, would appear to afford a favourable opportunity of verifying this hypothesis.

The Thermodynamics of a Strained Elastomer. I. General Analysis

1949 ◽  
Vol 22 (1) ◽  
pp. 64-78
Author(s):  
M. Mooney
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Thermodynamic Functions ◽  
Sufficient Accuracy ◽  
General Analysis ◽  
Partial Differential ◽  
Secondary Importance ◽  
General Validity ◽  
Mean Pressure ◽  
The Mean

Abstract The thermodynamic functions of principal interest in a strained elastomer are the entropy and energy of deformation. The volume is of secondary importance, and it can be assumed, with sufficient accuracy for most purposes, that the volume is linear in the temperature and the mean pressure. The basic partial differential equations of thermodynamics can then be integrated, yielding expressions for the energy and entropy of deformation in terms of observable quantities. In the present analysis the volume effects caused by changes in mean pressure and crystallinity are taken into account, and the effects associated with change in shape are sharply separated from those associated with change in volume. It is shown that the superelastic functions of deformation previously published have a very general validity.

scholarly journals XV. Invariants, convariants, and quotient-derivatives associated with linear differential equations

1888 ◽  
Vol 179 ◽  
pp. 377-489 ◽  
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Linear Character ◽  
Independent Variables ◽  
General Order ◽  
Independent Variable ◽  
The Subject ◽  
Linear Differential ◽  
Analytic Derivation

The present Memoir deals with a set of invariants and covariants of linear differential equations of general order. The set is proved to be complete, that is to say, every covariantive function of the same type can be expressed as a function of the members of the set, the only operations necessary for this expression being purely algebraical operations. The transformations, to which the differential equations are subjected, are supposed to be the most general consistent with the maintenance of their order and their linear character; they are, linear transformation of the dependent variable and arbitrary transformations of the independent variable. The covariantive property of the functions considered is constituted by the condition that, when the same functions are formed for the transformed equation, they are equal to the functions for the original equation, save as to a factor of the form ( dz / dx ) μ , where z and x are the two independent variables. The memoir, with the exception of a single and rather important digression, is occupied solely with investigations of the forms of the functions, of their interdependence, and of methods of construction. The earlier part deals chiefly with the synthetic derivation of the functions, the later part with their analytic derivation. Tables of the functions have not been calculated; in most cases the expressions of the functions are given in their forms as associated with the differential equation when it is taken in an implicitly general canonical form, and only in very few cases are functions given in connexion with an explicitly general form. Within these limits the subject of the memoir has been strictly confined; there is not, for instance, any attempt at classification of differential equations of the same order as discriminated by forms and values of invariants or covariants.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Applying Circle Game to Enhance Students’ Speaking Skill

2020 ◽  
Vol 7 (2) ◽  
pp. 119
Author(s):  
Putri Denaya Side Ayu ◽  
Heri Hidayatullah ◽  
Sri Ariani
Keyword(s):  
Action Research ◽  
Learning Process ◽  
Active Involvement ◽  
Post Test ◽  
Speaking Skill ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research ◽  
Speaking Skills

This Collaborative Classroom Action Research aimed at enhancing students’ speaking skill through the application of Circle Game. It was conducted in one cycle consisting of two meetings. The subject was the seventh of C class of SMPN 2 Alas Barat consisting of 22 students. The types of data were qualitative (acquiring observation during the learning process) and quantitative (speaking tests). The results qualitatively showed that the implementation of Circle Game enhanced the students’ speaking skills. Such improvement could be seen from their enthusiasm, their interesting feeling in various materials presented by the teacher, their active involvement. In the quantitative findings, the result also showed a higher value of the mean score of the post-test (77.34) rather than the pre-test (75.75). In conclusion, the use of Circle Game can improve students’ speaking skill.

UPAYA MENINGKATKAN HASIL BELAJAR IPA MELALUI PENGGUNAAN VIDEO PEMBELAJARAN BAGI SISWA KELAS IV DI SDN 187/IV KOTA JAMBI

2015 ◽  
Vol 8 (2) ◽  
pp. 93
Author(s):  
Juniar Siregar
Keyword(s):  
Action Research ◽  
Research Method ◽  
Research Report ◽  
The Third ◽  
The Media ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research

This study presents a research report on improving students’ Learning results on IPA through Video. The objective was to find out whether students’ learning result improved when they are taught by using Video. It was conducted using classroom action research method. The subject of the study was the Grade IV students of SDN 187/IV Kota Jambi which is located on Jln. Adi Sucipto RT 05 Kecamatan Jambi Selatan, and the number of the students were 21 persons. The instruments used were test. In analyzing the data, the mean of the students’ score for the on fisrt sycle was 65,4 (42,85%) and the mean on cycle two was 68,5 (37,15%) and the mean of the third cycle was 81,4 (100%). Then it can be concluded that the use of video on learning IPA can improve the students’ learning result. It is suggested that teachers should use video as one of the media to improve students’ learning result on IPA.Keywords : IPA, students’ learning result, video

THE USE OF COMMUNITY LANGUAGE LEARNINGMETHOD TO IMPROVE STUDENTS’ SPEAKING ACHIEVEMENT

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Eko Widoyo Putro ◽  
Berlin Sibarani
Keyword(s):  
Language Learning ◽  
Secondary Data ◽  
Primary Data ◽  
Second Grade ◽  
Learning Method ◽  
Field Notes ◽  
The Subject ◽  
The Mean ◽  
Method Improvement ◽  
Community Language

This study is aimed at improving the second grade of students’ speakingachievement by using Community Language Learning (CLL) Method. Theresearch was conducted by applying classroom action research. The subject of this study was second grade of Private Senior High School (Sekolah Menengah Atas Swasta) of Dwi Tunggal Tanjung Morawa which consisted of 31 students. To collect the data, the instruments used were primary data (SpeakingTest) and secondary data (interview sheet, observation sheet, field notes). It can be seen from the score in test I, test II and test III. In the Test I, the mean of the students’score was (64.77), in the Test II was (71.35), and the mean of the students’ score of the Test III was (80.90). Based on the interview, and observation sheet, it shows that the expression and excitement of the students got improved as well. It was found that teaching of speaking by using Community Language Learningcould significantly improve students’ speaking achievement.Key Words: Community Language Learning, Method, Improvement, Speaking Achievement

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