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Glossary for Multibody Simulation (MBS) and Multibody Dynamics (MBD)


A_DELNRM: The Accumulated Total Norm

A measure used in numerical algorithms, particularly iterative solvers, to track the convergence of a solution. In MBS, A_DELNRM represents the accumulated total norm of changes in the solution variables over iterations. Monitoring this value helps determine whether the solution is stabilizing and converging to an accurate result, which is critical for ensuring the reliability of the simulation outcomes.


A device that converts energy into motion, used to control a system or mechanism within a multibody simulation.

AINF: The Accumulated Total Number of Integration Failures

A metric that tracks the cumulative number of times integration fails during the simulation process. In MBS, integration failures can occur due to various reasons such as numerical instability, inappropriate time step size, or model inaccuracies. Monitoring AINF helps identify and address issues related to the integration process, ensuring the accuracy and stability of the simulation over time.


The process of evaluating simulation results to understand system behavior, identify issues, and optimize performance.

ANRF: The Accumulated Total Number of Newton-Raphson Failures

A metric that tracks the cumulative number of times the Newton-Raphson method fails to converge to a solution during the simulation process. In MBS, frequent Newton-Raphson failures can indicate issues with the stability or formulation of the model. Monitoring ANRF helps in diagnosing and addressing convergence problems, improving the reliability and robustness of the simulation.



The primary components in MBS, which can be rigid or flexible. Bodies interact through joints, forces, and other connections.

Boundary Conditions

Constraints applied to the system to define how it interacts with the environment or other systems.

Boundary Element Method (BEM)

A numerical computational method used to solve linear partial differential equations which have been formulated as integral equations. In the context of MBS, BEM is particularly useful for acoustic simulations. It allows for the efficient modeling of sound radiation and scattering, especially in problems involving infinite or semi-infinite domains such as exterior acoustic fields. BEM focuses on the boundaries of the domain, reducing the dimensionality of the problem and thus the computational effort required. This makes it an effective tool for simulating acoustic behaviors in complex multibody systems.


Computer-Aided Design (CAD)

The use of computer software to create, modify, analyze, and optimize a design. CAD tools enable engineers to develop precise 2D and 3D models of components and systems. In MBS, CAD models are often imported to create accurate representations of mechanical systems, providing a detailed geometric basis for simulation. CAD integrates with MBS software to streamline the workflow from design to analysis, ensuring that the physical characteristics and constraints of the design are accurately represented in the simulation.

Computer-Aided Engineering (CAE)

The use of computer software to aid in engineering analysis tasks. This includes simulations, optimizations, and evaluations of engineering designs. In the context of MBS, CAE tools are used to model, simulate, and analyze the dynamic behavior of complex systems, enhancing the design process by providing insights into system performance under various conditions. CAE encompasses a wide range of tools and technologies, including finite element analysis (FEA), computational fluid dynamics (CFD), and multibody dynamics (MBD).

Computational Fluid Dynamics (CFD)

A branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems involving fluid flows. In MBS, CFD is used to simulate the interaction between fluids (liquids and gases) and multibody systems, providing detailed analysis of aerodynamic and hydrodynamic forces.


The property of a material or system that allows it to deform under load. In MBS, this can refer to flexible bodies that deform under applied forces.


A limitation or condition that restricts the movement or forces within the system. Constraints can be applied through joints, contacts, or boundary conditions.


Mechanisms or algorithms used to manage the behavior of a system within an MBS, often involving feedback loops and actuators to maintain desired performance.


The process of integrating two or more simulation environments to work together, allowing different aspects of a system to be simulated simultaneously for more accurate and comprehensive analysis.



A force that reduces the amplitude of oscillations in a system. Damping can be modeled as linear or nonlinear in MBS.

Degrees of Freedom (DOF)

The number of independent movements a body can make. In MBS, each body has a certain number of DOFs, typically translational and rotational.

Design of Experiments (DOE)

A systematic method used to plan, conduct, analyze, and interpret controlled tests to evaluate the factors that may influence the performance of a system or process. In MBS, DOE is used to identify key variables and optimize system performance by exploring the effects of different design parameters.

Digital Twin

A digital replica of a physical system used to simulate, analyze, and optimize its performance. In the context of MBS, a digital twin integrates detailed multibody simulation models with data from the physical system to predict behavior, diagnose issues, and enhance decision-making. This technology helps in monitoring and improving the performance of mechanical systems, providing valuable insights for design, operation, and optimization throughout their lifecycle.



The ability of a material to return to its original shape after deformation. In MBS, elasticity is important for modeling flexible bodies.

Eigenvalue Analysis

A mathematical method used to determine the natural frequencies and mode shapes of a system.


Finite Element Method (FEM)

A numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It subdivides a large system into smaller, simpler parts called finite elements. This method is particularly useful in MBS for analyzing complex structures and systems where detailed stress, strain, and deformation analyses are required. FEM can handle nonlinearities in materials and large deformations, making it essential for modeling flexible bodies within MBS.

Flexible Bodies

Components in MBS that can deform under load. These bodies are modeled to capture realistic behaviors of materials and structures.

Force Element

An element in MBS that generates forces, such as springs, dampers, and actuators.

Frequency Response Analysis (FRA)

A technique used to determine how a system responds to different frequencies of input, typically in the form of vibrations or oscillations. In MBS, FRA is utilized to analyze and understand the dynamic behavior of systems under various frequency inputs, helping to identify resonance frequencies and improve the design for better performance and durability.


Graphical User Interface (GUI)

A user-friendly visual interface that allows engineers to interact with multibody simulation software. The GUI provides tools for modeling, simulating, and analyzing systems through graphical elements such as icons, buttons, and menus, making it easier to create complex models, run simulations, and interpret results without needing extensive programming knowledge.


A force that attracts bodies towards the center of the Earth. In MBS, gravity is often a key external force acting on the system.


h - Stepsize

The increment of time used in the numerical integration process of a simulation. The size of the step determines the resolution of the simulation results, with smaller stepsizes providing higher accuracy at the cost of increased computational effort. In MBS, choosing an appropriate stepsize is crucial for balancing precision and computational efficiency



The property of a body that resists changes in its state of motion. In MBS, inertia is defined by the mass and mass distribution of the body.


The numerical process of solving differential equations over time to simulate the behavior of the system.


Jacobian (Matrix)

A matrix that represents the partial derivatives of a set of functions with respect to a set of variables. In multibody simulation, the Jacobian matrix is used to describe how changes in the system's generalized coordinates affect the constraints and kinematic equations. It plays a crucial role in solving systems of nonlinear equations, optimizing performance, and ensuring the stability and accuracy of dynamic simulations.


A connection between two or more bodies that constrains their relative motion. Types of joints include revolute, prismatic, and spherical.



The study of motion without considering the forces that cause it. In MBS, kinematic analysis involves determining the positions, velocities, and accelerations of bodies.

Kinetic Energy

The energy a body possesses due to its motion. In MBS, kinetic energy is a key component of the system's dynamics.


Lagrange Multiplier

A mathematical technique used in multibody simulation to handle constraints. It involves introducing additional variables, called Lagrange multipliers, to transform a constrained optimization problem into an unconstrained one. This method is particularly useful for enforcing kinematic constraints in dynamic systems, ensuring that the motion of the bodies adheres to the specified constraints throughout the simulation.

Linear Analysis

An analysis method where the system's equations are linearized, often used for small deformations and simple systems.


An external force or moment applied to a body in the system. Loads can be static or dynamic.



A point or coordinate system attached to a body within a multibody simulation, used to track and define the position, orientation, and motion of that body or specific points on it. Markers are essential for applying constraints, forces, and interactions between bodies, as well as for measuring and outputting simulation results. They help in establishing relationships and references between different components in the system.

Meta Model

A simplified model that approximates the behavior of a more complex simulation model. In MBS, meta models are used to reduce computational costs and time by providing quick estimates of system responses. These models are typically generated through techniques such as surrogate modeling, response surface methodology, or machine learning. Meta models help in optimizing designs, conducting sensitivity analyses, and performing large-scale simulations where full-scale models would be computationally prohibitive.

Modal Analysis

A technique used to determine the natural frequencies and mode shapes of a system. Important for understanding vibration characteristics.

Multibody System

A system composed of multiple interconnected bodies whose dynamic behavior is studied in MBS.

Multistep Solver

A type of numerical solver that uses multiple steps to advance the solution of differential equations over time, improving accuracy by considering past information.


Newton-Raphson Method

An iterative numerical method used to solve nonlinear equations. In MBS, it is often employed to find equilibrium positions or to solve for unknown forces and displacements.

NJAC: The Total Number of Jacobian Evaluations

A metric used to quantify the number of times the Jacobian matrix is computed during a simulation. In MBS, frequent evaluations of the Jacobian matrix are necessary for solving the equations of motion, especially when dealing with nonlinear systems or iterative solvers. Monitoring NJAC helps assess the computational effort required and can be useful for optimizing the efficiency of the simulation process.

Nonlinear Analysis

An analysis method that considers nonlinearities in the system, such as large deformations, material properties, and contact conditions.

NRES: The Total Number of Residual Evaluations

A metric that indicates the total number of times residuals are computed during the simulation process. In MBS, evaluating residuals is essential for iterative methods to ensure that the solution converges accurately to the desired result. Monitoring NRES helps in understanding the computational effort involved and can provide insights into the efficiency and performance of the simulation.

Numerical Damping

An effect that arises from the integration process used in numerical simulations. It results in the artificial dissipation of energy within the system, which can help stabilize the simulation and reduce non-physical oscillations or instabilities. While not a physical property of the system, numerical damping is a byproduct of certain integration algorithms and time-stepping methods, and it can influence the accuracy and convergence of the simulation results.



The process of adjusting the design parameters of a system to achieve the best possible performance according to defined criteria. In MBS, optimization involves using algorithms to find the optimal configuration of system components, improving factors such as weight, strength, durability, and efficiency.


Potential Energy

The energy stored in a system due to its position or configuration. In MBS, potential energy is often associated with elastic elements like springs.


Reference Frame

A coordinate system used to define the positions, orientations, and motions of bodies within a multibody simulation. The reference frame provides a basis for measuring and describing the movement and interaction of all components in the system. It can be either inertial (fixed) or non-inertial (moving), and choosing an appropriate reference frame is crucial for accurately modeling the dynamics of the system.


The difference between the observed (or computed) value and the expected (or exact) value in a numerical solution. In MBS, the residual measures how well the current solution satisfies the system of equations. A smaller residual indicates a solution that closely matches the expected results, while a larger residual suggests discrepancies. Residuals are used to assess the accuracy and convergence of iterative solvers, with the goal of minimizing the residuals to achieve a precise solution.

Rigid Bodies

Components in MBS that do not deform under load. Rigid bodies are used to simplify the modeling of systems where deformations are negligible.



The process of using a computational model to study the behavior of a multibody system over time.

Single-Step Solver

A type of numerical solver that advances the solution of differential equations one step at a time, typically using only the current state information to determine the next state.


A set of instructions designed to perform a frequently used operation within a larger program. In MBS, subroutines can be used to customize simulations, define specific behaviors, or implement complex calculations.


Time Step

The increment of time used in the numerical integration process of a simulation. The size of the time step affects the accuracy and stability of the simulation.


A rotational force applied to a body. In MBS, torques can be generated by motors, actuators, or external forces.

Total Norm

A measure of the magnitude of a vector, typically used in the context of numerical solvers in multibody simulation. It represents the overall size of the vector that may include changes in positions, velocities, forces, or other relevant quantities. The total norm helps in assessing the convergence of iterative solutions by indicating how close the current solution is to the desired accuracy. Reducing the total norm to a small value is often a criterion for achieving convergence in simulation algorithms.

Transient Analysis

The study of a system's response to time-dependent inputs or conditions. In MBS, transient analysis involves simulating the behavior of the system over a specified period, capturing the dynamic changes and interactions between components. This type of analysis is crucial for understanding how a system responds to varying forces, motions, and environmental conditions over time. It is used to predict system performance, identify potential issues, and optimize designs for dynamic applications. Transient analysis helps in evaluating real-world scenarios such as start-up, shut-down, impact events, and varying load conditions.



The process of verifying that the simulation model accurately represents the real-world system it is intended to simulate.

Virtual Prototyping

The use of MBS to create and test digital models of mechanical systems before physical prototypes are built.