Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0000 362360 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0789 1211680 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0789 1211680 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1452 4104912 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1465 4138160 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1472 4155872 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1472 4172880 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1479 4180616 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1479 4180616 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1873 4477680 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1888 4495080 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1893 4516008 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1990 4616752 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1990 4617008 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Condition for a Plane Curve

If a particle moves along a curvesatisfyingthen the curve is a plane curve.

Ifthenis a linear combination ofandsofor some constants %alpha and %beta .

Integration gives

Rearrangement gives

The second order equation has independent solutionsandwhereare functions ofand are constant vectors.

Thenis the solution to