html,body{font-size:16px !important;line-height:18px !important;height:100%;color:#333;padding:0;margin:0}*,html,body{font-family:"Poppins",sans-serif;font-weight:normal;letter-spacing:normal;-webkit-font-smoothing:antialiased;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box;text-rendering:geometrirecision;-webkit-tap-highlight-color:rgba(0,0,0,0);outline:none !important;letter-spacing:-0.1px;word-wrap:break-word}.row{display:flex;flex-wrap:wrap;margin-left:-10px;margin-right:-10px;padding:0 2px}.col{flex:0 0 auto;width:25%;margin-bottom:20px;padding-left:10px;padding-right:10px}.col .entity-item{height:100%}strong,b{font-family:"Poppins",sans-serif;font-weight:bold}figure{margin:0;padding:0}a{text-decoration:none;color:#174fae}a:hover{text-decoration:underline}pre{padding:5px;margin-top:20px;background:#f3f3f3;border:1px solid #ccc}p{font-size:18px;line-height:24px}.link{cursor:pointer}.nowrap{white-space:nowrap}.overflow-auto{overflow:auto !important;-webkit-overflow-scrolling:touch !important}.h1,.h2,.h3,.h4,.h5,.h6,h1,h2,h3,h4,h5,h6{font-family:"Poppins",sans-serif;font-weight:bold}.multiple:after{content:',';margin-right:4px}.multiple:last-child:after{content:'';margin-right:0}.icon-home{display:flex;justify-content:center;align-items:center}.icon-home svg{fill:#fff;width:15px;height:15px}.icon svg{fill:#fff;width:35px;height:35px}.m-0{margin:0 !important}.p-0{padding:0 !important}.mt-0{margin-top:0 !important}.mb-0{margin-bottom:0 !important}.mb-2{margin-bottom:10px !important}.me-1{margin-right:5px !important}.me-2{margin-right:10px !important}.mb-4{margin-bottom:20px !important}.mt-2{margin-top:20px !important}.mt-1{margin-top:10px !important}.opacity-0{opacity:0 !important}hr{border:0;border-top:1px solid #ccc}.hide-scrollbar{overflow-x:scroll;scrollbar-width:none}.hide-scrollbar::-webkit-scrollbar{display:none}.d-none{display:none !important}.btn{display:inline-block;font-weight:400;line-height:1.5;color:#212529;text-align:center;text-decoration:none;vertical-align:middle;cursor:pointer;-webkit--select:none;-moz--select:none;-select:none;background-color:transparent;border:1px solid transparent;padding:.375rem .75rem;font-size:1rem;border-radius:.25rem;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}.btn:hover{text-decoration:none}.btn-link{font-weight:400;color:#0d6efd;text-decoration:none}.btn-group-sm>.btn,.btn-sm{padding:.25rem .5rem;font-size:.875rem;border-radius:.2rem}.btn-outline-dark{color:#212529;border-color:#212529}.btn-outline-dark a{color:#212529}.btn-outline-dark:hover{color:#fff;background-color:#212529;border-color:#212529}.btn-outline-dark:hover a{color:#fff;text-decoration:none}.btn-outline-light{color:#f8f9fa;border-color:#f8f9fa}.btn-outline-light:hover{color:#000;background-color:#f8f9fa;border-color:#f8f9fa}.btn-secondary{color:#fff;background-color:#6c757d;border-color:#6c757d}.btn-dark{color:#fff;background-color:#001c4c;border-color:#001c4c}.btn-danger{color:#fff;background-color:#dc3545;border-color:#dc3545}.btn-light{color:#000;background-color:#f8f9fa;border-color:#f8f9fa}.btn-rounded{border-radius:50px}.btn-dark:hover{color:#ccc}.btn-outline-dark{color:#212529;border-color:#212529}.btn-outline-dark:hover{color:#fff;background-color:#212529;border-color:#212529}.btn-movie{font-size:25px;line-height:25px;padding:0;border-radius:50% !important;width:60px;height:60px;margin:0 15px 0 0;display:flex;justify-content:center;align-items:center}.btn-movie svg{width:30px;height:30px}.btn-icon{line-height:0}.btn-icon svg{fill:#fff;width:1.1em;height:1.1em}.btn-movie:hover svg{fill:#fff}.breadcrumb{font-size:16px;line-height:30px}.breadcrumb{display:flex;flex-wrap:wrap;padding:0;margin-bottom:1rem;list-style:none}.breadcrumb-item+.breadcrumb-item{padding-left:.5rem}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:.5rem;color:#6c757d;content:"/";font-size:12px}.sidebar{display:flex;justify-content:space-between;height:100%;flex-direction:column}.sticky-box{height:100%;width:100%;margin-bottom:20px;padding:0}.banner{position:sticky;top:10px;margin-bottom:20px;margin-left:auto;margin-right:auto}.banner ins{position:sticky;top:10px;text-decoration:none;display:block;overflow:hidden !important}.banner ins:after{content:'PUBLICIDAD';background:#f5f5f5;width:100%;display:block;text-align:center;font-size:12px;line-height:12px;padding:4px 0}.bottom-ad-module{display:none}.roba-mobile{display:none}.roba-mobile,.roba-desktop{min-height:600px}.roba-desktop{display:flex;justify-content:start;align-items:end;flex-direction:column;width:320px;max-width:320px}.board-article-outbrain{margin-bottom:40px}.input-group{position:relative;display:flex;flex-wrap:wrap;align-items:stretch;width:100%}.input-group>.form-control,.input-group>.form-select{position:relative;flex:1 1 auto;width:1%;min-width:0}.input-group:not(.has-validation)>.dropdown-toggle:nth-last-child(n+3),.input-group:not(.has-validation)>:not(:last-child):not(.dropdown-toggle):not(.dropdown-menu){border-top-right-radius:0;border-bottom-right-radius:0}.input-group>:not(:first-child):not(.dropdown-menu):not(.valid-tooltip):not(.valid-):not(.invalid-tooltip):not(.invalid-){margin-left:-1px;border-top-left-radius:0;border-bottom-left-radius:0}.form-control{display:block;width:100%;padding:.375rem .75rem;font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;background-clip:padding-box;border:1px solid #ced4da;-webkit-appearance:none;-moz-appearance:none;appearance:none;border-radius:.25rem;transition:border-color .15s ease-in-out,box-shadow .15s ease-in-out}.form-control-sm{min-height:calc(1.5em+.5rem+2px);padding:.25rem .5rem;font-size:.875rem;border-radius:.2rem}.container{width:1140px;margin-left:auto;margin-right:auto}.top{margin-bottom:20px}.topbar-container{width:100%;background-color:#001c4c}.topbar{position:relative;display:flex;justify-content:center;padding:10px 0;z-index:2}.header-section{border-top:1px solid #fff;background-color:#eaede2;padding:10px 0;text-align:center}.header-section .header-section-title,.header-section .header-section-title a{font-family:"Poppins",sans-serif;font-weight:700;font-size:26px;line-height:26px;margin:0;padding:0;color:#001c4c}.menu-container{width:100%}.menu{position:relative;display:flex;justify-content:center;border-bottom:1px solid #ffffff59;padding:5px 0;z-index:2;background-color:#f3f3f3}.menu .navbar-nav{display:flex;flex-direction:row;list-style:none;padding:0;margin:0}.menu .navbar-nav .nav-link{display:block;padding:.5rem;text-decoration:none;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out;color:rgba(0,0,0,.55);font-weight:500;font-size:14px;line-height:14px;text-transform:uppercase}.form-search-container{padding:15px 0;width:auto;background-color:#e9f1f8}.form-search{display:flex;flex-direction:row;justify-content:center;width:1140px;margin-left:auto;margin-right:auto}.form-search form{display:flex;width:50%}.form-search .input-search-autocomplete{background-color:#ffffffa8}.section{width:100%;margin-bottom:40px}.section .section-header{display:flex;align-items:center;justify-content:space-between;border-top:3px solid #001c4c;border-bottom:1px solid #001c4c;margin-bottom:20px}.section .section-header p,.section .section-header h2,.section .section-header h1{font-size:24px;line-height:28px;font-weight:bold;color:#001c4c;font-size:24px;line-height:24px;padding:10px 0;margin:0}.entity-item{display:flex;flex-direction:column;position:relative;width:100%;border-bottom:4px solid #001c4c;background:#f3f3f3;box-shadow:0 0 4px #000;text-align:left;margin-bottom:0}.entity-item .entity-item-details{order:1;padding:10px}.entity-item .entity-title,.entity-item .entity-title a{font-size:18px;line-height:20px;font-family:"Poppins",sans-serif;font-weight:600;color:#333;text-decoration:none;margin-bottom:0;margin-top:0;text-transform:uppercase}.entity-item .entity-title small{font-size:14px;line-height:16px}.entity-item .entity-title a:before{content:"";top:0;left:0;right:0;bottom:0;display:block;margin:0;padding:0;position:absolute;z-index:2}.entity-item .entity-item-image{order:0}.entity-item .figure{position:relative;aspect-ratio:.66666667;display:flex;justify-content:center;align-items:center;background-color:#222;color:#fff;overflow:hidden}.entity-item .figure:after{content:var(--category-var);position:absolute;bottom:5px;right:5px;font-size:14px;line-height:14px;text-align:right;background:#2e579e;color:#fff;font-weight:bold;padding:3px 6px;border-radius:5px}.entity-item .figure .img{position:absolute;top:0;left:0;width:100%;height:100%;object-fit:cover}.footer{background-color:#001c4c;padding:20px 0}.footer .container{display:flex;flex-direction:column;justify-content:center;align-items:center;text-align:center}.footer p{font-size:14px;line-height:1;color:#fff;text-align:center;padding:0 10px}.footer a{color:#ccc}.gallery{display:grid;grid-auto-flow:column;grid-auto-columns:calc(100% / 1.1);gap:10px;overflow-x:scroll;scroll-snap-type:x mandatory;scroll-behavior:smooth}.gallery figure{scroll-snap-align:start;position:relative;aspect-ratio:16 / 9;border-radius:10px;border:1px solid #ccc;display:flex;justify-content:center;align-items:center;background-color:#222;color:#fff;width:100%}.gallery img{position:absolute;top:0;left:0;width:100%;height:100%;object-fit:cover;border-radius:10px}.video-gallery{display:grid;grid-auto-flow:column;grid-auto-columns:calc(100% / 1.1);gap:10px;overflow-x:scroll;scroll-snap-type:x mandatory;scroll-behavior:smooth}.video{scroll-snap-align:start;border-radius:10px;overflow:hidden}.video iframe{width:100%;height:100%;aspect-ratio:16 / 9}.entity-gallery .gallery-row>*{border:1px solid #ffffff00}.entity-gallery .gallery-row{display:grid;grid-auto-flow:column;grid-auto-columns:calc(100% / 4.06);gap:15px;overflow-x:auto;overflow-y:hidden;scroll-snap-type:x mandatory;scroll-behavior:smooth;scroll-padding:0}.entity-gallery .gallery-row-6{grid-auto-columns:calc(100% / 5.9)}.entity-gallery .gallery-column{width:100%;scroll-snap-align:start;object-fit:cover}.entity-gallery .entity-item{display:flex;flex-direction:column;position:relative;margin-bottom:0;height:100%}.carousel-wrapper{position:relative}.carousel-button{position:absolute;top:50%;transform:translateY(-50%);background-color:#00000099;color:white;border:0;padding:10px 10px;cursor:pointer;z-index:10;border-radius:100%;display:flex;justify-content:center;align-items:center}.carousel-button svg{fill:#fff;width:20px;height:20px}.carousel-prev{left:0}.carousel-next{right:0}.accordion{width:100%;border:1px solid #ccc;border-radius:8px}.accordion-item{border-top:1px solid #ccc}.accordion-header{display:flex;justify-content:start;align-items:center;padding:15px;cursor:pointer;font-weight:bold}.accordion-header .badge{background-color:#6c757d;color:#fff;padding:5px 10px;border-radius:4px;font-size:14px}.accordion-checkbox{display:none}.accordion-content{max-height:0;overflow:hidden;transition:max-height .3s ease;padding:0 10px;background-color:#fff}.accordion-checkbox:checked ~ .accordion-content{max-height:500vh;padding:0 10px}.accordion-content .table{width:100%;margin-top:10px;margin-bottom:10px;border-collapse:collapse}.accordion-content .table td{padding:10px;border:1px solid #ddd}.accordion-item:first-of-type{border-top:0}.accordion-header::after{flex-shrink:0;margin-left:auto;content:"+";background-repeat:no-repeat;background-size:1.25rem;transition:transform .2s ease-in-out}.accordion-header h4{font-weight:normal}.accordion-content p{margin-top:0}.no-disponible{text-align:center}@media(max-width:1024px){.container{width:100%}.top{margin-bottom:0}.other-container{width:100%;margin:0;padding-left:15px;padding-right:15px}.col{flex:0 0 auto;width:50%}.menu{display:block}.aside-container{display:none}.form-search{width:100%}.form-search form{display:flex;width:100%;margin:0 15px}.entity-item .entity-title,.entity-item .entity-title a{font-size:16px;line-height:18px}.breadcrumb{margin-bottom:10px;padding-left:15px;padding-right:15px}.gallery{grid-auto-columns:calc(100% / 1.1)}.entity-gallery .gallery-row{grid-auto-columns:calc(100% / 2.3)}.section .section-header p,.section .section-header h2,.section .section-header h1{font-size:20px;line-height:22px}.roba-desktop{display:none}.roba-mobile{position:relative;top:0;margin-bottom:30px;display:flex;justify-content:start;align-items:center;flex-direction:column;width:calc(100vw - 30px);max-width:calc(100vw - 30px)}.roba-mobile ins{position:sticky;top:0}.bottom-ad-module{display:block;position:fixed;bottom:0;left:0;width:100%;margin:0;box-shadow:0 -1px 5px 0 rgba(0,0,0,.2);text-align:center;line-height:0;background:#f5f5f5;z-index:3000004;transition:transform .5s ease,opacity .5s ease}.bottom-ad-module-hidden{transform:translateY(100%);opacity:0}.bottom-ad-module .publi-box__close-btn{display:block;color:#666;background:#f5f5f5;z-index:1000001;font-size:17px;padding:5px;box-shadow:1px -2px 2px 0 rgba(0,0,0,.2);border-top-left-radius:8px;width:28px;height:28px;position:absolute;top:-28px;right:0;cursor:pointer}} .article{width:100%}.movie-header{position:relative;margin-bottom:40px;display:flex;flex-direction:row;align-items:flex-start}.movie-header .figure{position:relative;aspect-ratio:.66666667;display:flex;justify-content:center;align-items:center;background-color:#222;color:#fff;width:250px;flex:0 0 250px;overflow:hidden;margin-right:20px}.movie-header .figure .img{position:absolute;top:0;left:0;width:100%;height:100%;object-fit:cover}.movie-title-container{margin:0 auto;z-index:1;flex:1 1 100%;overflow:hidden}.movie-title-container .title{border-top:4px solid #001c4c;border-bottom:1px solid #ccc;font-weight:bold;font-size:36px;line-height:38px;margin:0;padding:10px 0;margin-bottom:20px;color:#001c4c;text-transform:uppercase}.movie-title-container .author-name{margin-bottom:30px}.movie-title-container .author-name a{font-weight:normal;text-transform:uppercase}.movie-title-container .categories{position:absolute;bottom:0;margin-bottom:0}.movie-title-container .categories-relative{position:relative}.movie-title-container .categories a{margin-bottom:10px;margin-right:5px}.movie-title-container .tagline{margin-bottom:20px}.movie-buttons{display:flex;align-items:center;margin-bottom:20px}.movie-buttons .btn-buy{font-size:20px;line-height:1;font-family:sans-serif;font-weight:normal;text-transform:uppercase;height:60px;justify-content:center;align-items:center;display:flex;padding:0 30px;border-radius:30px}.movie-buttons .discountPercentage{font-size:22px;line-height:22px;font-weight:bold;color:green}.movie-container{display:flex;flex-direction:row}.movie-body{margin:0;width:780px;flex:0 0 780px;overflow:hidden}.aside-container{text-align:right;width:320px;flex:0 0 320px;position:relative;margin-left:40px}.providers{width:100%}.providers .provider-container{margin-bottom:20px}.providers a{margin-right:10px;display:inline-block}.providers a:last-child{margin-right:0}.providers img{width:55px;height:55px;border-radius:5px}.providers .provider-type{display:block;background:#eaede2;padding:5px;margin-bottom:10px;font-weight:bold}.providers .provider-container:last-child{margin-bottom:0}.movie-info .row-info{display:flex;flex-direction:row;margin-top:10px;margin-bottom:10px}.movie-info .col-title{font-size:18px;line-height:24px;width:40%;flex:0 0 40%;display:flex;align-items:center;margin:0;font-weight:normal}.movie-info .col-title .icon{display:flex;margin-right:5px}.movie-info .col-title .icon svg{width:20px;height:20px}.movie-info .col-value{width:60%;flex:0 0 60%}.movie-info .col-value p{padding:0;margin:0}.movie-info .col-value .link{white-space:nowrap;text-overflow:ellipsis;display:block;overflow:hidden}.movie-share{position:fixed;bottom:10px;right:10px;z-index:1000}.movie-share .btn{font-size:25px;line-height:25px;padding:0;border-radius:50% !important;width:60px;height:60px;display:flex;justify-content:center;align-items:center;background:#064cc3}.movie-share .btn svg{width:30px;height:30px;fill:#fff}.circle-wrap{width:60px;height:60px;background:#ccc;border-radius:50%;margin:0 15px 0 0;z-index:1}.circle-wrap .circle{position:relative}.circle-wrap .circle .mask,.circle-wrap .circle .fill{width:60px;height:60px;position:absolute;border-radius:50%}.mask .fill{clip:rect(0,30px,60px,0);background-color:#000}.circle-wrap .circle .mask{clip:rect(0,60px,60px,30px)}.circle-wrap .inside-circle{font-family:sans-serif;width:49px;height:49px;border-radius:50%;background:#064cc3;color:#fff;position:absolute;z-index:100;font-weight:700;font-size:18px;line-height:18px;top:5px;left:5px;display:flex;justify-content:center;align-items:center}@media(max-width:1024px){.movie-body{width:100%;flex:0 0 100%;overflow:unset}.movie-header{flex-direction:column}.movie-header .figure{margin:0;width:100%;flex:0 0 100%;background-color:transparent;aspect-ratio:unset;padding:20px 50px}.movie-header .figure .img{position:relative;height:auto;box-shadow:0 0 10px 0 #333}.movie-title-container{width:100%;margin:0;padding-left:15px;padding-right:15px;text-align:center}.movie-title-container .title{border-top:0;font-size:26px;line-height:30px;margin:0 0 20px 0}.movie-buttons{flex-direction:column;margin-bottom:30px;border-bottom:1px solid #ccc;padding-bottom:20px}.movie-buttons .btn-buy{margin-bottom:10px}.movie-title-container .categories{position:relative}.movie-container{margin:0;padding-left:15px;padding-right:15px}.movie-info .row-info{flex-direction:column}.movie-info .col-title,.movie-info .col-value p,.movie-info .col-value a{margin:0}.movie-info .col-title{width:100%;flex:0 0 100%;font-weight:600}.movie-info .col-value{width:100%;flex:0 0 100%}}
Aircraft Control Allocation Wayne Durham, Virginia Polytechnic Institute and State University, USA Kenneth A. Bordignon, Embry-Riddle Aeronautical University, USA Roger Beck, Dynamic Concepts, Inc., USA  An authoritative work on aircraft control allocation by its pioneers  Aircraft Control Allocation addresses the problem of allocating supposed redundant flight controls. It provides introductory material on flight dynamics and control to provide the context, and then describes in detail the geometry of the problem. The book includes a large section on solution methods, including 'Banks' method', a previously unpublished procedure. Generalized inverses are also discussed at length. There is an introductory section on linear programming solutions, as well as an extensive and comprehensive appendix dedicated to linear programming formulations and solutions. Discrete-time, or frame-wise allocation, is presented, including rate-limiting, nonlinear data, and preferred solutions.  Key features: Written by pioneers in the field of control allocation. Comprehensive explanation and discussion of the major control allocation solution methods. Extensive treatment of linear programming solutions to control allocation. A companion web site contains the code of a MATLAB/Simulink flight simulation with modules that incorporate all of the major solution methods. Includes examples based on actual aircraft.   The book is a vital reference for researchers and practitioners working in aircraft control, as well as graduate students in aerospace engineering