/** * This file represents an example of the code that themes would use to register * the required plugins. * * It is expected that theme authors would copy and paste this code into their * functions.php file, and amend to suit. * * @package TGM-Plugin-Activation * @subpackage Example * @version 2.3.6 * @author Thomas Griffin * @author Gary Jones * @copyright Copyright (c) 2012, Thomas Griffin * @license http://opensource.org/licenses/gpl-2.0.php GPL v2 or later * @link https://github.com/thomasgriffin/TGM-Plugin-Activation */ /** * Include the TGM_Plugin_Activation class. */ require_once dirname( __FILE__ ) . '/class-tgm-plugin-activation.php'; add_action( 'tgmpa_register', 'my_theme_register_required_plugins' ); /** * Register the required plugins for this theme. * * In this example, we register two plugins - one included with the TGMPA library * and one from the .org repo. * * The variable passed to tgmpa_register_plugins() should be an array of plugin * arrays. * * This function is hooked into tgmpa_init, which is fired within the * TGM_Plugin_Activation class constructor. */ function my_theme_register_required_plugins() { /** * Array of plugin arrays. Required keys are name and slug. * If the source is NOT from the .org repo, then source is also required. */ $plugins = array( // This is an example of how to include a plugin pre-packaged with a theme array( 'name' => 'Contact Form 7', // The plugin name 'slug' => 'contact-form-7', // The plugin slug (typically the folder name) 'source' => get_stylesheet_directory() . '/includes/plugins/contact-form-7.zip', // The plugin source 'required' => true, // If false, the plugin is only 'recommended' instead of required 'version' => '', // E.g. 1.0.0. If set, the active plugin must be this version or higher, otherwise a notice is presented 'force_activation' => false, // If true, plugin is activated upon theme activation and cannot be deactivated until theme switch 'force_deactivation' => false, // If true, plugin is deactivated upon theme switch, useful for theme-specific plugins 'external_url' => '', // If set, overrides default API URL and points to an external URL ), array( 'name' => 'Cherry Plugin', // The plugin name. 'slug' => 'cherry-plugin', // The plugin slug (typically the folder name). 'source' => PARENT_DIR . '/includes/plugins/cherry-plugin.zip', // The plugin source. 'required' => true, // If false, the plugin is only 'recommended' instead of required. 'version' => '1.1', // E.g. 1.0.0. If set, the active plugin must be this version or higher, otherwise a notice is presented. 'force_activation' => true, // If true, plugin is activated upon theme activation and cannot be deactivated until theme switch. 'force_deactivation' => false, // If true, plugin is deactivated upon theme switch, useful for theme-specific plugins. 'external_url' => '', // If set, overrides default API URL and points to an external URL. ) ); /** * Array of configuration settings. Amend each line as needed. * If you want the default strings to be available under your own theme domain, * leave the strings uncommented. * Some of the strings are added into a sprintf, so see the comments at the * end of each line for what each argument will be. */ $config = array( 'domain' => CURRENT_THEME, // Text domain - likely want to be the same as your theme. 'default_path' => '', // Default absolute path to pre-packaged plugins 'parent_menu_slug' => 'themes.php', // Default parent menu slug 'parent_url_slug' => 'themes.php', // Default parent URL slug 'menu' => 'install-required-plugins', // Menu slug 'has_notices' => true, // Show admin notices or not 'is_automatic' => true, // Automatically activate plugins after installation or not 'message' => '', // Message to output right before the plugins table 'strings' => array( 'page_title' => theme_locals("page_title"), 'menu_title' => theme_locals("menu_title"), 'installing' => theme_locals("installing"), // %1$s = plugin name 'oops' => theme_locals("oops_2"), 'notice_can_install_required' => _n_noop( theme_locals("notice_can_install_required"), theme_locals("notice_can_install_required_2") ), // %1$s = plugin name(s) 'notice_can_install_recommended' => _n_noop( theme_locals("notice_can_install_recommended"), theme_locals("notice_can_install_recommended_2") ), // %1$s = plugin name(s) 'notice_cannot_install' => _n_noop( theme_locals("notice_cannot_install"), theme_locals("notice_cannot_install_2") ), // %1$s = plugin name(s) 'notice_can_activate_required' => _n_noop( theme_locals("notice_can_activate_required"), theme_locals("notice_can_activate_required_2") ), // %1$s = plugin name(s) 'notice_can_activate_recommended' => _n_noop( theme_locals("notice_can_activate_recommended"), theme_locals("notice_can_activate_recommended_2") ), // %1$s = plugin name(s) 'notice_cannot_activate' => _n_noop( theme_locals("notice_cannot_activate"), theme_locals("notice_cannot_activate_2") ), // %1$s = plugin name(s) 'notice_ask_to_update' => _n_noop( theme_locals("notice_ask_to_update"), theme_locals("notice_ask_to_update_2") ), // %1$s = plugin name(s) 'notice_cannot_update' => _n_noop( theme_locals("notice_cannot_update"), theme_locals("notice_cannot_update_2") ), // %1$s = plugin name(s) 'install_link' => _n_noop( theme_locals("install_link"), theme_locals("install_link_2") ), 'activate_link' => _n_noop( theme_locals("activate_link"), theme_locals("activate_link_2") ), 'return' => theme_locals("return"), 'plugin_activated' => theme_locals("plugin_activated"), 'complete' => theme_locals("complete"), // %1$s = dashboard link 'nag_type' => theme_locals("updated") // Determines admin notice type - can only be 'updated' or 'error' ) ); tgmpa( $plugins, $config ); } Comments on: The Invisible Math Behind Aviamasters Xmas Flight Dynamics At first glance, flight appears effortless—wings glide, thrust propels, and gravity gently pulls. Yet beneath this grace lies a profound mathematical foundation, where vector calculus silently governs motion and forces. This invisible framework transforms abstract vectors into visible, predictable flight paths—now vividly illustrated through the real-world example of Aviamasters Xmas holiday flight dynamics. Foundations of Vector Calculus in Projectile Motion Vector calculus begins with Newton’s laws, decomposing motion into directional components. For projectile motion, velocity splits into horizontal (vₓ = v₀·cosθ) and vertical (v_y = v₀·sinθ) vectors. The parabolic trajectory emerges from combining constant horizontal speed with accelerated vertical motion under gravity. The path equation—y = x·tan(θ) – (gx²)/(2v₀²cos²θ)—reveals how angle θ and initial speed v₀ shape range and peak height. This equation reflects energy conservation: kinetic energy (½mv²) splits between horizontal momentum and vertical displacement, all governed by vector projections. Breaking velocity into components allows precise calculation of time of flight, maximum height, and landing range—critical for safe, efficient flight. Key VariableRole v₀Initial speed magnitude Determines trajectory extent and flight time θLaunch angle, dictating horizontal vs vertical force split gAcceleration due to gravity, driving vertical deceleration tan(θ)Horizontal velocity component scaling Kinetic Energy and the Physics of Vector Velocity Vector velocity is not just a directional arrow—it carries energy. Kinetic energy (½mv²) arises from the magnitude of velocity, which vector components directly influence. The horizontal component (vₓ) remains constant in ideal flight, preserving horizontal momentum, while the vertical (v_y) changes due to gravity. This decomposition shows how energy transforms: upward motion converts kinetic energy into potential energy, and vice versa during descent. Angle θ controls this balance—steeper θ angles favor height over range, altering energy distribution across the flight path. The 95% Confidence Interval: Quantifying Flight Uncertainty In real flight data, precision matters. Confidence intervals estimate likely ranges for velocity components or trajectory points by quantifying uncertainty, often using standard error and normal distribution assumptions. For Aviamasters Xmas flights, these intervals help anticipate variations in wind, thrust, or drag effects. For example, if horizontal velocity is measured at 12 m/s with ±0.4 m/s uncertainty, a 95% confidence interval spans 11.6 to 12.4 m/s—critical for safe navigation and collision avoidance. ParameterLower BoundUpper Bound Horizontal velocity (vₓ)11.612.4 Vertical velocity (v_y)–8.28.6 Aviamasters Xmas Flight: A Case Study in Vector Dynamics Aviamasters Xmas embodies vector calculus in holiday flight mode: a sleek drone navigating winter skies with precision. Its flight path is a vector-valued function—r(t) = ⟨v₀·cosθ·t, v₀·sinθ·t – ½gt²⟩—where time t integrates velocity and gravity into a smooth, predictable arc. Engineers model thrust, drag, and gravity as vector forces, adjusting flight computers in real time. Confidence intervals validate trajectory predictions, ensuring safe operation even amid gusts or system noise. Beyond the Basics: Hidden Mathematical Symmetries Projectile motion reveals elegant symmetries: time-reversal reverses velocity vectors, restoring symmetric flight profiles. Cosine and tangent define angular balance—cosθ governs horizontal reach, while tanθ shapes ascent symmetry. These insights empower autonomous systems, where vector math enables self-correcting navigation. Conclusion: From Theory to Flight Vector calculus is the unseen engine behind flight dynamics—translating abstract vectors into safe, efficient motion. Aviamasters Xmas offers a vivid, accessible case study: a modern holiday flight made real through timeless math. Understanding these principles deepens our grasp of aerospace engineering and fuels innovation in autonomous flight. Explore how energy, uncertainty, and motion converge in flight. For a firsthand look at vector dynamics in action, visit absolutely krass crash holiday mode. http://eliotzigmundjazz.com/2025/02/21/the-invisible-math-behind-aviamasters-xmas-flight-dynamics-p-at-first-glance-flight-appears-effortless-wings-glide-thrust-propels-and-gravity-gently-pulls-yet-beneath-this-grace-lies-a-profound-mathem/ Veteran Jazz Drummer Thu, 08 Nov 2018 09:20:05 +0000 hourly 1 https://wordpress.org/?v=5.0.22