Described herein are wireless smart devices having integrated force, position, acceleration, and rotational sensing for science education (e.g., Newton's laws of motion, kinematics, etc.). An integrated wireless device includes an accelerometer to generate acceleration data based on detecting a current rate of acceleration of the integrated wireless device, a shaft encoder to detect angular positional changes of a shaft or axle of the integrated wireless device over time, and at least one processing unit coupled to the accelerometer. The at least one processing unit is configured to decode angular position data of the shaft encoder into positional data and to synchronize acceleration data received from the accelerometer with the positional data. In one example, a force load cell is coupled to the at least one processing unit. The force load cell measures applied force or impact force.

Methods of and systems for executing a simulation of a constrained multi-body system. The method comprises, using a physics engine, simulating the constrained multi-body system, wherein: the constrained multi-body system comprises articulated constraints, the articulated constraints are associated with a geometric stiffness matrix; the geometric stiffness matrix defining a geometric stiffness; a diagonal approximation of the geometric stiffness matrix is generated; and the diagonal approximation is used as part of a stability analysis in which damping is automatically adjusted so that the damping stabilizes the simulation of the constrained multi-body system.

Methods of and systems for executing a simulation of a constrained multi-body system. The method comprises, using a physics engine, simulating the constrained multi-body system, wherein: the constrained multi-body system comprises articulated constraints, the articulated constraints are associated with a geometric stiffness matrix; the geometric stiffness matrix defining a geometric stiffness; a diagonal approximation of the geometric stiffness matrix is generated; and the diagonal approximation is used as part of a stability analysis in which damping is automatically adjusted so that the damping stabilizes the simulation of the constrained multi-body system.

A pulley system educational aid includes a portable standing and self-supporting frame with workstations. Each workstation is sized and positioned for one or more persons to manipulate pulley systems. Each workstation includes at least one pulley bar accessible by one or more persons near the workstation. The pulley arrangement can include a fixed pulley system, a movable pulley system, or a compound pulley system.

Model elements of an executable model, representing a physical system, are partitioned into one or more linear portions and one or more nonlinear portions. Simulating behavior of the physical system, by executing the model, includes, for each of multiple simulation time intervals, for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the model. A scattering matrix corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system. The correlation matrix is derived from the scattering matrix based on noise within the portion of the physical system. Noise sources representing noise within the portion of the physical system are identified based on the correlation matrix. At least one characteristic of noise associated with each noise source is computed, and noise characteristics are output at selected ports.

Model elements of an executable model, representing a physical system, are partitioned into one or more linear portions and one or more nonlinear portions. Simulating behavior of the physical system, by executing the model, includes, for each of multiple simulation time intervals, for a first nonlinear portion, computing a correlation matrix characterizing noise associated with one or more ports of the model. A scattering matrix corresponds to a portion of the physical system represented by the first nonlinear portion without accounting for any noise within the portion of the physical system. The correlation matrix is derived from the scattering matrix based on noise within the portion of the physical system. Noise sources representing noise within the portion of the physical system are identified based on the correlation matrix. At least one characteristic of noise associated with each noise source is computed, and noise characteristics are output at selected ports.

An apparatus and a method for demonstrating a new scientific discovery made by the inventor about the nonlinear instability of vehicles, like aircrafts, automobiles and ocean vehicles. The apparatus comprises a model and a three-gimbaled framework that permits the model to respond to inertial moments about the axes of which the moments of inertias are the smallest and the largest. In these two axes, the apparatus has restoring and damping capabilities. The apparatus also comprises external driven mechanisms to rotate the model about the intermediate principal axis of inertia. A method with closed form formulas for the external driven frequencies and amplitudes to be used to excite the nonlinear instabilities of the model is given. The model could be an aircraft, an automobile, a ship, or even a rectangular block.

An apparatus and a method for demonstrating a new scientific discovery made by the inventor about the nonlinear instability of vehicles, like aircrafts, automobiles and ocean vehicles. The apparatus comprises a model and a three-gimbaled framework that permits the model to respond to inertial moments about the axes of which the moments of inertias are the smallest and the largest. In these two axes, the apparatus has restoring and damping capabilities. The apparatus also comprises external driven mechanisms to rotate the model about the intermediate principal axis of inertia. A method with closed form formulas for the external driven frequencies and amplitudes to be used to excite the nonlinear instabilities of the model is given. The model could be an aircraft, an automobile, a ship, or even a rectangular block.

Described herein are wireless smart devices having integrated force, position, acceleration, and rotational sensing for science education (e.g., Newton's laws of motion, kinematics, etc.). An integrated wireless device includes an accelerometer to generate acceleration data based on detecting a current rate of acceleration of the integrated wireless device, a shaft encoder to detect angular positional changes of a shaft or axle of the integrated wireless device over time, and at least one processing unit coupled to the accelerometer. The at least one processing unit is configured to decode angular position data of the shaft encoder into positional data and to synchronize acceleration data received from the accelerometer with the positional data. In one example, a force load cell is coupled to the at least one processing unit. The force load cell measures applied force or impact force.

Described herein are wireless smart devices having integrated force, position, acceleration, and rotational sensing for science education (e.g., Newton's laws of motion, kinematics, etc.). An integrated wireless device includes an accelerometer to generate acceleration data based on detecting a current rate of acceleration of the integrated wireless device, a shaft encoder to detect angular positional changes of a shaft or axle of the integrated wireless device over time, and at least one processing unit coupled to the accelerometer. The at least one processing unit is configured to decode angular position data of the shaft encoder into positional data and to synchronize acceleration data received from the accelerometer with the positional data. In one example, a force load cell is coupled to the at least one processing unit. The force load cell measures applied force or impact force.