Penetrator Trajectory Control via Euler Coriolis Acceleration
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Solution Overview
Problem
Current technologies fail to accurately determine the rotational properties and in-flight path of ballistic projectiles, known as Penetrators, during Terraflight through high-density media, as they rely on simplified models that do not account for the unique dynamics of high-density Terramedia, leading to inaccuracies in guidance and control.
Innovation Solution
The use of Euler's Coriolis acceleration and a non-inertial polar reference frame to solve the rotational rigid body vector equation of motion, allowing for real-time determination of angular acceleration, velocity, and path, using a single axial accelerometer and AC coupling algorithms to differentiate and integrate sensor data, thereby overcoming the limitations of previous models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If simplified aerodynamic models are used for Penetrator flight through high-density media, then device complexity is reduced, but measurement precision and reliability of rotational property determination deteriorate
Solution Approach 1:
The patent changes the fundamental parameters of the mathematical model from aerodynamic equations to Euler's rotational rigid body vector equation, incorporating the Euler Coriolis acceleration term (2ω×vr) to accurately represent the physics of high-density media penetration. This parameter change transforms the model from incorrectly assuming aerodynamic dominance to correctly accounting for Euler Coriolis acceleration dominance, thereby resolving the contradiction between model simplicity and measurement accuracy.
2Ease of operation
If traditional aerodynamic reference frames are used, then ease of operation is maintained, but measurement precision of angular path and rotational variables deteriorates
Solution Approach 1:
The patent introduces a new dimension to the reference frame analysis by identifying and utilizing a second non-inertial polar reference frame that rotates with the Penetrator. This dimensional addition allows the system to capture the Euler Coriolis acceleration effects that are invisible in traditional inertial or body-fixed frames, thereby improving angular path determination accuracy while maintaining operational feasibility through systematic frame transformation.
3Device complexity
If Euler's rotational rigid body vector equation is solved without the Euler Coriolis acceleration term, then device complexity is reduced, but reliability of trajectory construction deteriorates
Solution Approach 1:
The patent extracts and isolates the Euler Coriolis acceleration term (2ω×vr) from the full Euler rotational equation, treating it as a distinct and dominant component that must be separately accounted for in high-density media penetration. By extracting this term and focusing computational resources on accurately resolving its effects in the rotating reference frame, the system achieves reliable trajectory construction without requiring excessive computational complexity across all equation terms.
4Reliability
If real-time rotational property determination is implemented, then guidance and control capability is improved, but device complexity and computational requirements increase
Solution Approach 1:
The patent performs preliminary action by establishing the correct theoretical framework and reference frame transformations before real-time data processing begins. By pre-defining the Euler Coriolis acceleration relationships and the rotating reference frame mathematics, the system reduces real-time computational complexity to primarily measuring angular variables and applying predetermined transformation equations, thereby enabling real-time guidance and control without excessive device complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables precise tracking and guidance of Penetrators by dynamically deploying Terrafoils to correct their trajectory, ensuring accurate targeting and penetration through high-density media by accurately modeling the rotational dynamics and path within the complex Terramedia environment.
Implementation Method 1
using a single axial accelerometer and AC coupling algorithms to differentiate and integrate sensor data
Implementation Method 2
Euler's 2ωXvr (bold face equation terms are vectors while non bolded terms are scalers) and post Euler named the Coriolis acceleration
Data Source
AI summary
Methods, systems, and devices solving Euler's rotational rigid body equation of motion, formed within two non-inertial frames of reference, that determine the vector inconstant variables of angular acceleration, velocity, and trajectory using a single piezoresistive accelerometer sensor, an ΔC coupling algorithm and 1st and 2nd running integrals to in-flight acquire rotational inconstants in high-density Terramedia Terraflight and determine a Penetrator's loading profiles and method to parse vector Terraflight for rotational Pitch and Yaw enabling precision trajectory tracking utilizing three axial facing piezoresistive accelerometers, a differencing algorithm and 1st and 2nd running integrals enabling Penetrator flight control and precision guidance.