Peter Zipfel

Modeling and Simulation Technologies · Research

A brief introduction to my advanced course on Tensor Flight Dynamics

Take your missile or rocket to your virtual test range, that is your computer. Before you do, take my course, and learn all about how to model missiles and rockets at fidelities that approach the real world with its six-degrees-of-freedom and uncertainties. Start with my C++ simulations and modify them for your concepts.

Get challenged by my post-graduate course on flight dynamics, activated by my high-fidelity simulations of missiles, aircraft, and hypersonic vehicles with their aerodynamics, propulsion, autopilots, guidance, and INS/GPS navigation.

In this 45 min video I give an overview of a UAV design course, where students, instead of building model airplanes, use their laptops to design and flight test their prototype designs.

CADAC being an open-source environment has attracted many users in academia and industry, while I used it at the Air Force Research Laboratory to develop several high-fidelity simulations, as well as at my company Modeling and Simulation Technologies. In twelve sections I will explain CADAC and its architecture: • I will show you how I use the pow...

Using C++ in aerospace simulations CADAC++ framework explained Building a net-centric multiple UAV, target and satellite simulation Adaptation of a University of Florida lecture

The Covariance Principle of General Relativity promotes the new tensor formulation of classical flight dynamics. After a brief introduction to Einstein's Relativity, this seminar outlines the foundation of Tensor Flight Dynamics, its 50 year history, and its major contributions to the flight sciences, while Einstein's love for the violin is echoing...

The universal Covariance Principle leads to the formulation of flight dynamics in tensors, invariant under all coordinate transformations. Once the phenomenological part is formulated in tensors, coordinate systems are introduced, which convert the tensors into matrices for computation. This approach: ”from tensor modeling to matrix programming” ha...

"The Tensor Flight Dynamics Tutor" is a condensed PowerPoint presentation of my textbook "Introduction to Tensor Flight Dynamics". It serves as a review of the main elements of tensor flight dynamics and can be used in the class room by professor and students. The download is unrestricted, so share it freely.

Virtual flight testing is all the rage these days: "Use your computer to demonstrate the veracity of your brainchild!" If you are into missiles and rockets, I teach you how these high fidelity simulations are built, validated, and used for performance tests. This workshop, with its 330 commented PowerPoint slides, is based on my five decades of exp...

*** In eight sessions you apply the power of C++ to a net-centric UAV simulation. As you study the more than 250 PowerPoint slides you use polymorphism, inheritance, and encapsulation to create a multi-object simulation on your Windows based computer, consisting of UAVs, targets, and satellites. *** This workshop is the condensed version of a cours...

Stay at home and study flight dynamics in six degrees-of-freedom. You fly missiles, aircraft, and hypersonic vehicles on your Windows based laptop, while experiencing the power of C++. Others have taken this workshop in the classroom in three days; you may take it at your leisure in three weeks.

*** Flight dynamics is shifting from vectors to tensors in order to adapt to the ever-increasing computer power available for solving complex aerospace problems. Computers love to chew on matrices, which are the counterparts of tensors. The physics of flight dynamics are modeled first by tensors independent of coordinate systems. Then, for computat...

Tensor flight dynamics solves flight dynamics problems using Cartesian tensors, which are invariant under coordinate transformations, rather than Gibbs’ vectors, which change under time-varying transformations. Three tensors of rank two play a prominent role and are the subject of this paper: moment of inertia, rotation, and angular velocity tensor...

Treat yourself to a book that combines theory with application. The operational equations of GPS/INS and star-tracker are derived and embedded into a three-stage solid rocket booster. Instead of hardware, you use a high fidelity simulation in C++, which launches the rocket and places a payload into low orbit. This six degrees-of-freedom simulation...

The culmination of the AIAA Self Study Series on modeling and simulation (M&S) is this course on high fidelity aerospace simulations. If you have mastered Peter Zipfel’s previous publications, or if you are a professional working in M&S, you will profit from this interactive training on advanced aerospace systems in C++. In 20 Labs you learn how to...

Now you can take a graduate course in high-fidelity aerospace vehicle M&S without sitting in the classroom at the University of Florida. Both student and teacher can use this course to interact with aircraft and missile simulations, proceeding from simple ballistic trajectories to controlled and guided flight. Assuming familiarity with aerospace sy...

How to model the orbital insertion of a payload in a high fidelity simulation is summarized in this paper. Though executed frequently in real time, actual flight software is inaccessible to a broader audience, and too complex for analytical studies. For exploratory trade studies of a three-stage solid rocket booster, the ascent guidance law is deri...

Modeling and Simulation of Aerospace Vehicle Dynamics, Third Edition unifies all aspects of flight dynamics for the efficient development of aerospace vehicle simulations. It provides the reader with a complete set of tools to build, program, and execute simulations. Unlike other books, it uses tensors for modeling flight dynamics in a form invaria...

Apply the power of C++ to aerospace vehicle simulations with this self-study course and take advantage of its multi-object feature to model interacting UAVs with satellites and targets. Building on your basic understanding of C++ and your familiarity with flight dynamics, you take a course taught at the University of Florida, learn from the PowerPo...

Are you in a hurry? Review these essentials of C++ before you read my simulation documents

In today’s network-centric world, aerospace vehicles interact with many objects. They navigate by overhead satellites, synchronize their flight paths with other vehicles, swarm over hostile territory and attack multiple targets. Studying these engagements with high-fidelity constructive simulations has become an important task of modeling and simul...

Tensor flight dynamics models flight dynamics with Cartesian tensors that are invariant under all coordinate transformations, even time dependent transformations. It elevates Newton's Second Law to a law that is not only invariant under inertial coordinate transformations, but under all transformations, thus bringing Newtonian mechanics under the u...

Modeling dynamics with tensors is a fruitful field, and was first applied to flight mechanics. It is based on the Covariance Principle that states that physical laws are independent of coordinate systems. Application to robotic manipulators portends that the equations of motion are derived without the use of coordinate systems. Cartesian tensors ar...

The C++ computer language is well suited to model multi-vehicle engagements. Its prowess is exemplified by the conversion of a unmanned aerial vehicle simulation from FORTRAN to C++. The new architecture accommodates besides UAVs and moving targets also targeting satellites. Its class structure is outlined, and the communication bus between the enc...

Summary of CADAC development up to 2006

In this paper, the state-dependent Riccati equation (SDRE) control method is used to design a guidance law for the midcourse phase of flight of a hypersonic vehicle. The guidance law converts flight path angle and heading angle commands to angle of attack and bank angle commands for input to an attitude autopilot

A technique is developed thai takes advantage of the inherent configurational symmetries of aircraft and guided missiles to eliminate some force and moment derivatives. Starting with the Principle of Material Indifference, tensor analysis is employed to derive two simple conditions for vanishing aerodynamic derivatives. The results apply to derivat...

A tensor formalism is introduced for the concise presentation of the equations of motion of flight vehicles. Two new concepts, the rotational time derivative and the generalized Euler transformation, enable a formulation of the equations of motion that is invariant under time-dependent coordinate transformations. Several dynamic equations are deriv...

The classical scalar perturbations of flight mechanics are compared with total vector perturbations. A component perturbation method is introduced which is the generalization of the classical technique, and is valid for all coordinate systems. This method, together with a new tensor formalism, is used to derive the general perturbation equations of...

A Magnus rotor is an autorotating flight vehicle, designed to develop a Magnus force efficiently and to employ it as the major lift force in free flight. The equations of motion of Magnus rotors are derived and their performance and stability analyzed and correlated with free flight tests. Necessary and sufficient conditions for limit cycles are de...