Lagrange Equations with Mathematica

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The original PL1/FORMAC computer program of my Diploma work (capable of running on an IBM-360 mainframe) was ported by myself to Mathematica in 2013. I want to publish these results on this Web site. An additional download will enable the motivated visitor of this site to reproduce the work with that program.

Theoretical Basics

The Lagrange Equations serve in the classical Mechanic the description of the motion of holonomic systems of rigid bodies. They are formally seen ordinary differential equations of the order 2, which are linear in the second order and quadratic in the first one. They have appropriate to my Diploma work the following form:

$g_{ρ ν} {\ddot{q}}^{v} + Γ_{ρ μ ν} {\dot{q}}^{μ} {\dot{q}}^{v} = Q_{ρ} ρ = 1 (1) f$

The metric g and the CHRISTOFFELsymbols Gamma as well as the generalized forces Q are calculated in the program published here. The input consists of an input file with a well defined format, which contains amongst others the following data:

the number of degrees of freedom and the number of the rigid bodies
the kinematics of the rigid bodies
linear springs and dampers connected to the rigid bodies
other applied forces and moments of force

Supplied Files

The following files are contained in the ZIP file provided for Download:

a folder Mechanics containing a complete Mathematica application including calculation module, initialisation module and complete documentation
a Mathematica notebook serving as interface to the user, see the preview
a sample input file demonstrating the structure of input
a sample output file generated from the given input

The notebook (and the module) is well documented and runs under Mathematica 7+.

Details: Category: Langrange Equations with Mathematica; Published: 08 May 2015; Hits: 5835

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SELECT a.params FROM jos_advancedmodules AS a WHERE a.module_id = 100407μs520B/plugins/system/advancedmodules/src/Helper.php:159Copy
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SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)1.01ms6.23KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
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SELECT SUM(CASE WHEN `a`.`next_execution` <= :now THEN 1 ELSE 0 END) AS due_count,SUM(CASE WHEN `a`.`locked` IS NULL THEN 0 ELSE 1 END) AS locked_count FROM `jos_scheduler_tasks` AS `a` WHERE `a`.`state` = 1491μs1.37KBParams/administrator/components/com_scheduler/src/Model/TasksModel.php:465Copy
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Lagrange Equations with Mathematica

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